NDUCTIVE LOGIG 



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Ballantine 




LIBRARY OF CONGRESS. 



Cliap.Ac..'_, Copyright No.,. 
Shelf_.B-2j 



UNITED STATES OF AMERICA. 



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Inductive Logic 



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WM. G. BALLANTINE 

President of Oberlin College 



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Boston, U.S.A., and London 

GINN & COMPANY, PUBLISHERS 

18.96 






THE LlBRAItY 
OF CONGRfiftft 

WA9HINGTOII 



Copyright, 1896 
By WM. G. BALLANTINE 



ALL RIGHTS RESERVED 




PREFACE, 



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This book originated in the class-room, where the 
author was teaching Dr. Fowler's Elements of Induc- 
tive Logic. Its ambition is to reproduce some of the 
excellences of that bright and interesting book, while 
substituting a sounder analysis of fundamental princi- 
ples. The numerous extracts, introduced in the man- 
ner of Dr. Fowler, are designed both to elucidate the 
subject and to acquaint the student with the views and 
literary styles of a large variety of philosophical and 
scientific writers. Wherever anything has been found 
already well expressed, quotation has been preferred to 
restatement. The familiar manuals of inductive logic 
have been freely drawn upon, and their rich store of 
illustrations has been used without hesitation. Credit 
has generally been given ; but sometimes it was impos- 
sible to make specific acknowledgment. 

Mr. Mill is the greatest of all modern writers upon 
inductive logic, and upon his famous work all later 
authors have largely built. The school manuals are, 
for the most part, but outlines of his doctrine. But 
Mr. Mill's mind was a very peculiar one. It was impos- 
sible for one so acute not to see the truth, or for one so 



iv Preface. 

candid not to state it. But these statements of truth 

are rather his obiter dicta, while his main contention is 

often some paradox. A "higher critic" might easily 

divide the Logic into two documents, by authors of 

opposing tendencies. An outline of Mill's system, like 

Dr. Fowler's, does him injustice ; for it is just in what 

he thinks most important, that he is weakest. Freely 

acknowledging that most of what is true in this book 

has been learned from Mr. Mill, the author yet puts it 

forth with the hope that it will be found to contain a 

real, though small, contribution to the progress of 

science. 

Oberlin, Ohio, 

December i, 1895. 



CONTENTS. 



-^2-^ 



CHAPTER I. 
Introductory 



Inductive Logic defined, i. The pure sciences, i. The applied 
sciences, 2, Inductive and Deductive Logic not mutually exclusive, 2. 
Relations of Inductive and Deductive Logic, 3. The discovery of facts 
defined, 4. Quotation from Whately, 4. 



CHAPTER II. 

Facts 6 

A fact defined, 6. Substantive facts and facts of relation, 6. Facts of 
Resemblance, 7. Facts of Coexistence, 7. Facts of Causation, 7. Facts 
of Succession, 8. Ultimate facts, 8. 

CHAPTER III. 

Observation 9 

Observation defined, 9. Bagon quoted, 9. Observation the essential 
characteristic of Induction, 9. Observation and Experiment contrasted, 

10. Fowler quoted, 10. Difficulty of making trustworthy observations, 

11. Dr. Darwin's supposed gin, 11. Confusion of perceptions and in- 
ferences, 12, 

CHAPTER IV. 
Primary Inductions 14 



An Induction defined, 14. Various kinds of inductions, 14. Uniform- 
ities in the existing order, 15. How we discover a uniformity, 15. The 
mill and stream, 16. Cliffs and crows of England, 17, Does induction 
rest upon the veracity of God ? 17. Inductio per Enwnerationetn Sim- 
plicem, 17. Correcting one generalization by another, 19. Uniformity 
of Nature defined, 19. Degrees of assurance in primary inductions, 20. 



vi Contents. 



PAGE 

Bain's definition of induction, 21. Bain's view discussed, 23. Great 
inductions of modern science, 24. Empirical and ultimate laws, 25. The 
maxim that " the exception proves the rule," 25. 



CHAPTER V. 

Secondary Inductions 28 

A secondary induction defined, 28, Primary and secondary inductions 
mingled in every-day thinking, 29. Whately provided only for secondary 
inductions, 30. Uniformity of all nature not a necessary premise, 31. 
Failure of philosophers to recognize three classes of inductions, 31. 
Minto's criticism of Mill, 33. Inferring from particulars to particu- 
lars, 34. 

CHAPTER VI. 

Mixed Inductions 36 

A mixed induction defined, 36. Masts of ships seen first, 36. Newton's 
discoveries, 36. The phases of Venus, 37. Mill's questions, 38, In- 
duction from a single instance, 39. Correctly defining the field, 40. 

CHAPTER VII. 

P^ACTS OF Resemblance 41 

Resemblances in objects, 41. The possibility of language, 42. Argu- 
ments from facts of resemblance, 42. Anima and dme^ 43. Genesis of 
the horse, 44. 

CHAPTER VIII. 
Facts of Coexistence 47 

Illustration from gold, 47. Coexistence as important as Causation, 47. 
Natural kinds and artificial kinds, 48. Infima species and stmimum 
ge7ius, 49. The true nature of species discussed by Asa Gray, 49. 
Agassiz's view, 50. Darwin's view, 5 1 . Linnaeus's definition, 51. Classi- 
fication, 52. Nomenclature, 53. Terminology, 53. 

CHAPTER IX. 

Facts of Causation and Facts of Succession . . .55 
Causation defined, 55. Count Rumford's experiment, 56. Rumford's 
experiment discussed, 59. Energetic cause, 60. Conditional cause, 61. 
Material cause^ 61. Volitional cause, 62. Lotze on the authority of 



Contents. vii 

PAGE 

causal law, 63. Things may cause events, 64. Events may cause events, 
65. Historical cause, 66. Events and states, 67. Occasional causes, 68. 
Incident in the life of Dr. Darwin, 69. Formal cause and final cause, 70. 
Negative cause, 70. Summing up of discussion of causation, 71. Do 
like causes produce like effects ? 72. Facts of succession not ultimate, 72. 



CHAPTER X. 

Mr. Mill's Doctrine of Causation 75 

Mill's eminence, 75. Notion of cause the root of the whole theory of 
induction, 75. Uniformity of nature not the immediate major premise, 
76. Deiinition of cause, ']']. All conditions equal, 78. Cause the sum 
total of conditions, 80. Cause and effect not necessarily successive, 83. 
Succession not between single antecedents and consequents, 85. Cause 
the total of immediately preceding conditions, 85. Unconditionalness, 85. 
Night not the cause of day, 86. The will under the law of causation, %"]. 



CHAPTER XL 

Canons for Isolating Facts of Causation . . . .91 

Comprehensive cause defined, 91. Mechanical isolation, 92. Isolation 
in thought, 93. Canon for Test of Difference, 93. Empirical cause, 93. 
Four cases under the canon, 94. Expression of cases in symbols, 97. 
Use of the facts isolated, in making inductions, 98. Canon for Test of 
Agreement, 99. Schiller on moral decline and aesthetic culture, 100. Ex- 
pression of cases in symbols, loi. The Plurality of Causes, 102. 



CHAPTER Xn. 

Mr. Mill's Four Experimental Methods .... 103 

The methods are fundamentally two, 103. The five canons, 104. The 
method of residues the same as the method of difference, 106. All the 
methods deductive, 106. Correction of instances, 107. The term " experi- 
mental," 107. Vagueness of terms and results, 107. Failure to hold fast 
the idea of sequence, 108. Investigation of crystallization, 108. Is the 
noun or the verb the cause ? 109. The joint method of agreement and 
difference an illusion, 109, Investigation of the cause of dew, no. Method 
of concomitant variations not distinct, iii. Mill exaggerates the im- 
portance of the methods, 112. Difference between ancient and modern 
thought, 113. 



viii Contents. 



CHAPTER XIII. 

PAGE 

Hypothesis 115 

Hypothesis defined, 115. Theory, 115. No explanation of uniform- 
ities, 116. The " laws of. nature," 116. Incident in the life of Darwin, 117. 
Rules for legitimacy of hypotheses, 118. Vera causa, 118. Mill's defini- 
tion, 119. Discovery of planet Neptune, 120, Darwin's theory of coral 
islands, 121. Helmholtz on forming hypotheses, 124. Whewell on the 
Greek physical philosophy, 125. Davis on function of hypothesis, 126. 
Value of false hypotheses, 127. 



CHAPTER XIV. 

Inductive Arguments 129 

Analogy, 129. Bishop Butler on probability, 129. Analogy a variety 
of primary induction, 130. Asa Gray on trees, 130. Robinson Crusoe, 
133. The Cincinnati glacial dam, 133. Analysis of Wright's argument, 
135. Verification, 136. Trials at law, 138. Testimony to observation, 
139. Hume on the grounds for accepting testimony, 139. Relevancy, 142. 

CHAPTER XV. 

Fallacies 146 

Bacon's " idols," 146. Non-observation or Prejudice, 150. Aristotle on 
the skull, 151. Bacon on wooden arrows, 152. Authority, 152. Modern 
teaching not dogmatic, 153. Scheiner and the. sun spots, 154. Partial 

Observation, or Neglect of Negative Instances, 154. Example from 

Brachet, 154. The Greek aorist, 156. The definition of a verb, 157. 
Signs of the weather, 157. Malobservation, 158. Mistake in Area, 159. 
"Adjacent cases," 159. The Indian prince, 159. Hume's mistake, 160. 
The law of motion, 160. Mistake in Isolation, 160, Experiment of Van 
Helmont, 161. Post hoc, ergo propter hoc, 162. Mutuality of Cause and 
Effect, 163. 

CHAPTER XVI. 

The Work of Bacon 165 

Lord Macaulay on Bacon, 165. Reid's opinion, 165. Bacon's claim, 
166. Minto's estimate, 167. Mill's criticism, 168. 



INDUCTIVE LOGIC 



CHAPTER I. 
INTRODUCTORY. 

Inductive Logic is the Science of the Discovery of 
Facts not directly observable. A few facts are known 
to us without discovery. Such are our personal iden- 
tity, moral freedom, and obligation. Certain truths 
also are recognized by the mind as certain as soon as 
they are suggested. Evidence is not required to 
establish them, nor can it in any w£.y confirm them. 
Of these are the axioms of Mathematics and the 
canons of Deductive Logic. This furniture is the 
same for all minds and the possession of it is what 
makes thinking possible. Only all minds do not with 
equal clearness analyze their own operations, and the 
most lack the patience, concentration, and strength 
to follow admitted principles to their ultimate con- 
sequences. 

Whole sciences have been built up by simply 
developing the necessary implications of the few 
simple but universal truths intuitively perceived by 
every mind. Deductive Logic and Mathematics are 
examples. One peculiarity of them is that they are 
the same for all minds, and that when the terms used 



2 Inductive Logic. 

are precisely understood there is no difference of 
opinion possible among sane men. These are pure 
sciences; they do not depend upon the actual exist- 
ence of any person or thing, but we know that whatever 
does exist, necessarily conforms to them. If numbers 
or quantities of objects exist anywhere, they are in 
mathematical relations; if correct thinking upon any 
subject is done by rational beings anywhere, it i& done 
according to the rules of deductive logic. 

But the great bulk of our knowledge does not come 
to us by intuition. Beyond the few facts and truths 
with which the mind starts, lies the whole universe of 
reality, which we can know only through observation. 
Over against the pure sciences stand the applied sci- 
ences. The main value of the pure sciences is in the 
fact that they furnish the principles for constructing 
the applied sciences. The latter have no new formal 
principles of their own. 

This last point is of supreme importance for the 
purpose now in hand. It has been extensively sup- 
posed that the field of thinking was divided into two 
kingdoms, ruled by two sovereigns. Deductive and 
Inductive Logic, under dissimilar constitutions, and 
that what was bad law in one kingdom might be good 
law in the other. It has been assumed that sometimes 
two thoughts which could show no right to union in 
the domain of Deduction could cross the border and, 
by a sort of Gretna Green marriage, make a synthesis 
in the kingdom of Induction. A little reflection should 
have shown all this to be a huge mistake. The canons 
of deductive logic are the universal laws of thought. 
They are invariably true, if ever true. The only 



Introductory. 3 

ground upon which we assent to any principle in 
deductive logic is our instant perception of its neces- 
sary and universal validity. If so, we cannot step into 
another province and escape its force. The limits of 
its domain are the same as those of correct thinking. 

Deductive and Inductive Logic are not two sister 
sciences which divide the empire of thinking between 
them. They are not mutually exclusive ; one does not 
stop where the other begins. One is not the inverse 
of the other. One does not proceed from generals to 
particulars, while the other moves from particulars to 
generals. It is not true that one infers from the 
known to the known, while the other infers from the 
known to the unknown. It is not true that one is 
rigorously required to draw conclusions no wider than 
its premises, while the other is warranted in concluding 
the universal from a part. Many such assertions have 
been made by philosophers, but it is obvious without 
discussion that, if there is any truth in deductive logic, 
all these assertions are false ; for deductive logic sways 
a universal scepter or none. There can be no legiti- 
mate thinking except according to its laws. Inductive 
Logic is simply deductive logic regulating our reason- 
ing upon our observations of the phenomena of the 
universe. It is deductive logic applied in the realm of 
reality. Whenever in our thinking a proposition is 
introduced the truth of which depends not upon its 
harmony with a previous admission, but directly upon 
observation, there our reasoning becomes Inductive. 
There is no new way of inferring peculiar to Induction. 
Deductive logic deals with the mutual harmony of 
propositions. Inductive logic deals with the harmony 



4 Inductive Logic. 

between propositions and facts. No reasoning of any 
kind, deductive or inductive, can ever carry knowledge 
a step forward into the unknown, or do anything more 
than unfold what is contained in the premises. 

We can learn the unknown only by observation ; we 
can reason upon our observations in no other way than 
deductively ; for that is the only way men can reason 
at all. The rational action of the mind upon the data 
of observation is called Induction. 

In defining Inductive Logic as the science of the 
Discovery of Facts we use the word discovery in the 
strictest sense, as meaning the ascertainment of the 
absolutely unknown. 

To quote from Archbishop Whately : — - 

" There certainly are two kinds of ' New Truth ' and of 
' Discovery,' if we take those words in the widest sense in which 
they are ever used. First, such truths as were, before they were 
discovered, absolutely unknown, being not implied in anything we 
previously knew, though we might perhaps suspect them as 
probable ; such are all matters of fact strictly so-called, when 
first made known to one who had not any such previous knowl- 
edge as would enable him to ascertain them a priori^ /.<?., by 
reasoning ; as, if we inform a man that we have a colony at 
Botany Bay ; or that the earth is such a distance from the sun ; 
or that platina is heavier than gold. The communication of this 
kind of knowledge is most usually and most strictly called infor- 
mation; we gain it from observation^ and from testi7nony j no 
i7iere internal ^vor kings of our own minds (except when the mind 
itself is the very object to be observed), or mere discussions in 
words will make these known to us ; though there is great room 
for sagacity in Judging what testimony to admits and forming 
conjectures that may lead \.o profitable observation^ and to experi- 
ments with a view to it. The other class of Discoveries is of a 
very different nature. That which may be elicited by Reasoning, 



Introductory. 5 

and consequently is implied in that which we already know, we 
assent to on that ground, and not from observation or testimony : 
to take a geometrical truth upon trust, or to attempt to ascertain 
it by observation, would betray a total ignorance of the Science." ^ 

In the following treatise we shall first inquire what 
is meant by "a fact," and shall then follow as exactly 
as possible the processes of mind by which facts are 
ascertained. The several fallacies to which the unwary 
are exposed will receive a large share of attention. 
The points to be considered will require hard thinking, 
but if any advance in clearness is made, the labor will 
be well repaid ; for inductive thinking is the largest 
part of the work of life. 

1 Whately's Logic, p. 216. 



CHAPTER II. 
FACTS. 

Since Inductive Logic is the science of the Dis- 
covery of Facts, it is necessary to consider at the 
outset what is meant by a fact. The human mind 
finds itself in a universe of phenomena. Through the 
senses it has perceptions of an external world, and 
through consciousness it knows its own modifications. 
Through these channels alone can the mind advance in 
knowledge of realities. Whatever has real existence 
is a fact. It may be a substance, an energy, a quality, 
an action, a state, or only some relation of substances, 
energies, qualities, actions, or states, but if it be 
perceived by the mind it is a fact. A dragon is not a 
fact, because it is not perceived; but the notion of a 
dragon is a fact, for that is an action of the mind of 
which I am conscious. The sun is a fact, the continent 
of America is a fact; the yellow color of gold, the 
attraction of a magnet, the likeness of two peas, are 
facts. 

For the purposes of induction, facts may be classi- 
fied as substantive facts and facts of relation. A 
substantive fact is a phenomenon considered apart, as 
independently existing. The yellowness of gold, the 
weight of gold, the malleability of gold, are substantive 
facts. A fact of relation connects in some way two 
substantive facts. That malleability and yellowness 
coexist in gold is a fact of relation. 



Facts. J 

Facts of relation are of three kinds: Facts of 
Resemblance, Facts of Coexistence, and Facts of 
Causation. Facts of Succession are often named 
among the ultimate kinds, but, as we shall see later, 
they are dependent upon simpler facts of causation. 

One of the first lessons received by a child when it 
begins, as we say, to notice, is that there are many 
things in the world which resemble one another. 
Often the resemblance is so complete that the several 
phenomena seem but repetitions of the same thing. 
Thus from the observation of individual facts we pass 
through the perception of resemblances to the forma- 
tion of a general concept. Common nouns are but the 
names of indefinite numbers of facts that resemble one 
another. The possibility of language arises from the 
constant repetition of similar things for which the 
same words will do. 

It is also observed that there are certain more or less 
constant groups of substantive facts. We repeatedly 
find yellowness, sweetness, roundness, etc., coexisting ; 
and to this assemblage of phenomena we give the 
name orange. We find yellowness, malleability, spe- 
cific gravity 19.32, etc., coexisting, and we call this 
group of coexistences gold. 

It is observed that when certain substantive facts or 
groups of substantive facts are in a certain collocation, 
a reaction occurs between them and that this is often 
attended by a change in one or more of the facts or 
groups. The relation between facts or groups of facts 
and their reactions, as well as the relation between any 
fact or group of facts and itself in a new form, is called 
Causation. 



8 Inductive Logic. 

Further it is observed that certain substantive facts 
appear in succession; thus, after a ball is struck, we 
see it move; after a bell is swung, we hear a sound; 
after we touch fire, a smart follows. The relation by 
which an antecedent fact is linked to a consequent one 
we call Succession. Careful attention to the facts of 
succession is a large part of the work of science, since 
it is in most cases impossible to bring immediately 
into existence the phenomena which we desire; we 
produce them indirectly by producing their antecedents. 

We do not know why certain simple facts coexist or 
why certain phenomena resemble each other or why 
certain things react as they do. These are ultimate 
facts of the Universe. There is no law of thought 
necessitating them; consequently they belong wholly 
to the domain of Induction. That the most refrangible 
rays of light have a violet color, and that the least 
refrangible rays have a red color, are facts for which no 
one expects ever to know a reason. Science makes 
no progress in this direction. 



CHAPTER III. 



OBSERVATION. 



The first step in the discovery of facts is always 
Observation. In order to know what is passing in 
our own minds or in the external world, we must give 
attention. Each act of attention is called an Observation. 
To quote the words of Bacon : " Man, being the servant 
and interpreter of Nature, can do and understand so 
much, and so much only, as he has observed in fact or 
in thought of the course of nature : beyond this he 
neither knows anything nor can do anything." ^ The 
five senses report to the mind the world of matter and 
force ; consciousness interprets to the thinking subject 
his own activities. Perception and consciousness sup- 
ply the materials out of which the structure of Inductive 
Science is built up. But thought can build nothing 
without the use of those primary facts and necessary 
truths which are known by intuition without the process 
of discovery. There is nothing peculiar in any process 
of inference in inductive investigation ; for by the 
nature of the mind there can be but one mode of 
inference, namely that of deduction. The element of 
observation is the essential characteristic of Induction. 
Any syllogism is inductive in which one of the premises 
formulates the observation of some fact. The great 
work of Bacon was just this, that he with singular 

1 Works, vol. viii, p. 67. 



lO IndiLctive Logic. 

clearness, persuasiveness, and charm of language called 
mankind to patient observation of Nature. 

A distinction is sometimes made between Observa- 
tion and Experiment. Dr. Fowler says : — 

" To observe is to watch with attention phenomena as they 
occur ; to experiment (or, to adopt more ordinary language, to per- 
form ail experiineiif) is not only to observe, but also to place the 
phenomena under pecuHar circumstances, as a preHminary to 
observation. Thus every experiment implies an observation, but 
it also implies something more. In an experiment, I arrange or 
create the circumstances under which I wish to make my observa- 
tion. Thus, if two bodies are falling to the ground, and I attend 
to the phenomenon, I am said to observe it, but if I place the 
bodies under the exhausted receiver of an air-pump, or cause them 
to be dropped under any special circumstances whatever, I may- 
be said not only to make an observation, but also to perform an 
experiment. Bacon has not inaptly compared experiment with the 
torture of witnesses. Mr. Mill distinguishes between the two 
processes, by saying that in observation we find our instance in 
nature, in experiment we make it, by an artificial arrangement of 
circumstances."^ 

All this is very clear: indeed, it is so clear that one 
is surprised that the discussion of experiments did not 
come up in connection with a classification of instances, 
as natural and artificial. The fact that we can make 
instances artificially is of great importance in the 
progress of science ; but it is not properly the basis of 
any distinction regarding the act of observation, which 
is always the same whatever the origin of the instance. 
There is no more contrast between an observation and 
an artificial instance than there is between an observa- 
tion and a natural instance. Nor is the difference 

1 Inductive Logic, p. 40. 



Observation. 1 1 

between natural and artificial instances, that is, between 
experiments and instances which are not experiments, 
always clearly traceable. All of the arrangements of 
human life and society are artificial ; we learn from 
them to our cost, and often, in consequence, change our 
methods. Popular government is frequently spoken of 
as still an experiment ; the construction of our armored 
battle ships is experimental. Yet instances of this 
kind are not arranged for the sake of learning from 
them, although with the expectation of learning, and 
improving. 

The primary rule for any inductive thinking is to 
make sure of the observations. Starting with preju- 
dices, guesses, or inferences, the truth never can be 
reached. Nothing but observation can establish a 
hitherto unknown fact. The explanation of the slow 
advance of science in ancient and mediaeval times may 
be found mainly in the neglect of this simple rule. In 
spite of many errors in methods of thinking, the men 
of those times would have discovered a vast body of 
facts, if they had only given attention to them. 

But the making of a precise and trustworthy observa- 
tion is by no means the easy thing which at first it 
seems to be. Very much of what passes for observa- 
tion is merely mistaken inference. An amusing illus- 
tration occurs in Charles Darwin's recollections of his 
father : — 

" He himself never drank a drop of any alcoholic fluid. This 
remark reminds me of a case showing how a witness under the 
most favorable circumstances may be utterly mistaken. A gentle- 
man-farmer was strongly urged by my father not to drink, and 
was encouraged by being told that he himself never touched 



12 IndiLctive Losric 



i> 



spirituous liquor. Whereupon the gentleman said, ' Come, come, 
Doctor, this won't do — though it is very kind of you to say so for 
my sake — for I know that you take a very large glass of hot gin 
and water every evening after your dinner.' So my father asked 
him how he knew this. The man answered, ' My cook was your 
kitchen-maid for two or three years, and she saw the butler every 
day prepare and take to you the gin and water.' The explanation 
was that my father had the odd habit of drinking hot water in a 
very tall and large glass after his dinner ; and the butler used first 
to put some cold water in the glass, which the girl mistook for gin, 
and then filled it up with boiling water from the kitchen boiler." i 

To quote from Dr. Fowler : — 

" That which is strictly matter of perception does not admit of 
being called in question ; it is the ultimate basis of all our reason- 
ing, and, if we are to repose any confidence whatever in the exercise 
of our faculties, must be taken for granted. But there are few 
of our perceptions, even of those which to the unphilosophical 
observer appear to be the simplest, which are not inextricably 
blended with inference. Thus, as is well known to every student 
of psychology, in what are familiarly called the perceptions of 
distance and of form, the only perception proper is that of the 
various tints of color acting on the retina of the eye, and it is by 
a combination of this with perceptions of touch, and the muscular 
sense, that the mind gains its power of determining form and 
distance. Now, a judgment of this kind, which is really due to 
inference, is, especially by the uneducated and unreflecting, per- 
petually mistaken for that which is due to direct observation ; 
and thus what is really only an inference from facts is often 
emphatically asserted to be itself a matter of fact." ^ 

To quote from Mr. Mill : — 

" One of the most celebrated examples of a universal error 
produced by mistaking an inference for the direct evidence of the 
senses, was the resistance made, on the ground of common sense, 

^ Life and Letters, p. 15. ^ Inductive Logic, p. 273. 



Observation. • 13 

to the Copernican system. People fancied that they saw the sun 
rise and set, the stars revolve in circles round the pole. We know 
that they saw no such thing ; what they really saw was a set of 
appearances, equally reconcilable with the theory they held and 
with a totally different one. It seems strange that such an instance 
as this of the testimony of the senses pleaded with the most entire 
conviction in favor of something which was a mere inference of 
the judgment, and, as it turned out, a false inference, should not 
have opened the eyes of the bigots of common sense, and inspired 
them with a more modest distrust of the competency of mere 
ignorance to judge the conclusions of cultivated thought. 

"In proportion to any person's deficiency of knowledge and 
mental cultivation is, generally, his inability to discriminate between 
his inferences and the perceptions on which they were grounded. 
Many a marvelous tale, many a scandalous anecdote, owes its 
origin to this incapacity. The narrator relates, not what he saw 
or heard, but the impression which he derived from what he saw 
or heard, and of which perhaps the greater part consisted of 
inference, though the whole is related not as inference but as 
matter of fact. The difficulty of inducing witnesses to restrain 
within any moderate limits the intermixture of their inferences 
with the narrative of their perceptions, is well known to experienced 
cross-examiners ; and still more is this the case when ignorant 
persons attempt to describe any natural phenomenon. " The 
simplest narrative,' says Dugald Stewart, 'of the most illiterate 
observer involves more or less of hypothesis ; nay, in general, it 
will be found that, in proportion to his ignorance, the greater is 
the number of conjectural principles involved in his statements. 
A village apothecary (and, if possible, in a still greater degree, an 
experienced nurse) is seldom able to describe the plainest case, 
without employing a phraseology of which every word is a theory: 
whereas a simple and genuine specification of the phenomena 
which mark a particular disease, a specification unsophisticated 
by fancy, or by preconceived opinions, may be regarded as 
unequivocal evidence of a mind trained by long and successful 
study to the most difficult of all arts, that of the faithful interpreta- 
tion of nature.' " ^ 

1 Logic, p. 545. 



CHAPTER IV. 



PRIMARY INDUCTIONS. 



An Induction is a generalization, or an inference, 
based upon propositions that state observed facts. The 
truth inferred may be general or particular, but it must 
be one which we cannot perceive in a single act of 
observation. When we know the existence of anything 
by simply attending to it, we do not say that we know 
it inductively ': we know it directly. The word Induc- 
tion is applied both to the proposition enunciated and 
to the process of mind by which that proposition is 
reached. That "all men are mortal," I know by induc- 
tion, and the truth is itself an induction. 

Inductions are based either wholly upon observations, 
in which case we call them Pure Inductions ; or they 
are based partly upon observation and partly upon 
intuitively known truth, in which case we call them 
Mixed Inductions. Pure inductions are either Com- 
plete or Incomplete, according as we have or have not 
observed all the facts included in the statement. They 
are either Primary or Secondary, according as they 
are made directly by generalizing a number of observa- 
tions, or indirectly by combining syllogistically a single 
new observation with a previous induction. These 
distinctions will become clear as we advance. The 
present chapter deals with Primary Inductions. 

It soon becomes plain to every child, when he begins 
to observe the world, that there is an existing order of 



Primary hiductions. 15 

things. It is perfectly easy to conceive of a world in 
which every object should be unique and every event a 
surprising novelty. Such a world would contradict no 
necessity of thought, although it would be hopelessly 
bewildering. But such is not our world. The child's 
earliest impression is of a certain permanence and uni- 
formity in its environment. The same objects and 
experiences remain or recur. 

This conviction of an existing order finds expression 
in language. The present tense in grammar does not 
denote a mere moment separating the past and the 
future ; it denotes a considerable and indefinite expanse 
of time. Such a proverb as " The burnt child shuns 
the fire " is stated in the present tense, as formulating 
a fact of the existing order. 

That experience falls largely into lines of uniformity 
is early perceived. The child learns that there are 
things called apples which are round and red and good 
to eat, and that there are things called cats which have 
soft fur and long tails and sharp claws, and that these 
things are liable to scratch. The profoundest question 
in the whole science of inductive logic is : How are 
these generalizations reached t How can we ever dis- 
cover that we are upon the line of a uniformity } But 
this is really only a sort of metaphysical puzzle, like 
the question of the possibility of motion. The exist- 
ence of lines of uniformity is every moment forced 
upon our observation, and the fact that they do extend 
is equally conspicuous. 

A Primary Induction is the statement of an observed 
uniformity. Do we reach it by any process of infer- 
ence } Philosophers have thought so. There is thought 



1 6 Inductive Lozic. 



i3 



to be here a new and peculiar kind of inference of 
which deductive logic knows nothing. Professor Davis 
says : " Induction is an immediate synthetic inference 
generalizing from and beyond experience." ^ But this 
does not appear to be a correct analysis. When there 
is an inference we necessarily look about for proposi- 
tions which can be syllogistically combined. Professor 
Davis claims that we intuitively know the Uniformity 
of Nature, and he unconsciously makes this his major 
premise. But the uniformity of nature can be known 
and defined only inductively, not intuitively. It is a 
discovery of induction, not the basis of it. 

No : if there is a permanent or recurring fact in 
nature, we ascertain it simply by generalization, not by 
inference. 

How do we know that the mill is standing by the 
river t We cannot be looking at it all of the time. 
Having seen it a hundred or a thousand times we have 
come to believe in its permanence. How do we know 
that the water is flowing over the mill-dam } We have 
seen it often and have come to' think it continuous. 
Here is a permanent fact — the mill, and a uniformity 
— the flow of the water ; how do we come to feel 
assured of them } Not by any process of inference, but 
simply by generalization. We have not reasoned about 
the future or the unknown, but about the present and 
the known. Whether the world will come to an end 
to-night, and the river and the mill be annihilated, we 
cannot predict from our observations upon them ; all 
that we know is that this permanence — the mill, and 
this uniformity — the flow of the stream, are facts of 

1 Inductive Logic, p. 6. 



Primary Inductions. ij 

the existing order ; and since it would be irrational to 
act, without evidence, upon the supposition of the 
cessation of the existing order, we keep on carrying 
grist to the mill. 

A primary induction does not rest upon a process of 
inference any more than does our belief in any per- 
manent fact. That the cliffs of England are white is 
a permanent fact ; that the crows of England are black 
is a uniformity. We cannot be looking at the cliffs all 
the time, and we cannot examine all the crows ; but 
having looked at the cliffs frequently, and having seen 
a large number of crows, we rest in the assurance that 
we know the existing order. Should we wake up some 
morning and find the cliffs blackened, we should simply 
recognize that the order had changed. Should we find 
in visiting a remote part of the kingdom a flock of 
white crows, we should simply observe that we had 
passed beyond the former area of observation. If our 
expectation of finding the cliffs white and the crows 
black at the next observation rested upon any logical 
necessity, our not finding them so would require a doubt 
of our own sanity. 

The suggestion has been made that we base our 
belief in the truth of a primary induction upon our 
faith in the veracity of God. But surely such an induc- 
tion as that " the Cretans are always liars " cannot be 
based upon the veracity of God ; it rests merely upon 
observation of the uniform mendacity of those depraved 
people. 

The sort of induction we are now describing has been 
known, since Bacon's time, as Inductio per Enume- 
rationem Simplicem, Induction by Simple Count. "It 



1 8 Inductive Logic. 

consists in ascribing the character of general truths to 
all propositions which are true in every instance that 
we happen to know of." Mr. Mill's attitude toward 
such inductions in the first edition of his Logic was 
curious. Although holding that the uniformity of 
Nature, the law of Causation, and the axioms of Mathe- 
matics are established only in this way, he yet inclined 
to deny to the process even the name of induction. He 
said : " This is the kind of induction, if it deserves the 
name, which is natural to the mind when unaccustomed 
to scientific methods." Later Mr. Mill omitted the 
clause "if it deserves the name"; but his disparaging 
tone continued and infected logical writers. Thus, 
Dr. Fowler says : — 

" But not only is the htductio per Enuinerationem Sijnplicem 
the mode of generalization natural to immature and uninstructed 
minds ; it is the method which, till the time of Bacon, or at least 
till the era of those great discoveries which shortly preceded the 
time of Bacon, was almost universal." " When men first begin 
to argue from their experience of the past to their expectation of 
the future, or from the observation of what immediately surrounds 
them to the properties of distant objects, they seem naturally to 
fall into this unscientific and unreflective mode of reasoning." ^ 

Bacon himself seems responsible for this sneer ; he 
says : — 

" Inductio quae procedit per enumerationem simplicem, res 
pueriHs est, et precario concludit, et periculo exponitur ab instantia 
contradictoria, et plerumque secundum pauciora quam par est, et 
his tantum modo quae praesto sunt pronunciat." ^ 

Still there remains an inconsistency in Mr. Mill's 
doctrine ; for he says most justly : — 

1 hiductive Logic, pp. 280, 281. 2 JSfovum Orgamim, lib. i, aph. cv. 



Primary IndiLctions. 19 

" Experience must be consulted in order to learn from it under 
what circumstances arguments from it will be valid. We have no 
ulterior test to which we subject experience in general ; but we 
make experience its own test. Experience testifies, that among 
the uniformities which it exhibits or seems to exhibit, some are 
more to be relied on than others ; and uniformity, therefore, may- 
be presumed from any given number of instances, with a greater 
degree of assurance, in proportion as the case belongs to a class 
in which the uniformities have hitherto been found more uniform. 
This mode of correcting one generalization by another, a narrower 
generalization by a wider, which common sense suggests and 
adopts in practice, is the real type of scientific induction." ^ 

The truth could not be better set forth than in the 
foregoing accurate and discriminating statement ; after 
all, the "real type of scientific induction" is merely an 
indiictio per enumerationeni simplicem, carefully made. 

Experience gives us not only uniformities, but uni- 
formities among uniformities. Not only does this ox 
uniformly chew the cud, but all oxen uniformly chew 
the cud, and all other sorts of animals with similar 
structure uniformly chew the cud. Not only does this 
piece of lead maintain a uniform specific gravity of 
1 1.4, but there is a uniformity in specific gravity among 
all pieces of lead, and, moreover, every different sub- 
stance maintains a uniform specific gravity. What we 
call the "Principle of the Uniformity of Nature" is 
merely the wide primary induction that the various 
limited uniformities of nature persist. There is no 
other sense in which nature is uniform. It is not 
meant, of course, that every object is like every other 
object, and every event like every other event. 

1 Logic, p. 232. 



20 Inductive Logic. 

" Every person's consciousness assures him that he does not 
always expect uniformity in the course of events ; he does not 
always beUeve that the unknown will be similar to the known, 
that the future will resemble the past. Nobody believes that the 
succession of rain and fine weather will be the same in every 
future year as in the present. Nobody expects to have the same 
dreams repeated every night. On the contrary everybody mentions 
it as something extraordinary, if the course of nature is constant, 
and resembles itself in these particulars. To look for constancy 
where constancy is not to be expected, as for instance that a day 
which has once brought good fortune will always be a fortunate 
day, is justly accounted superstition." ^ 

The assurance with which a primary induction is 
held, depends upon the number of instances from which 
it is generalized. If the number is small, the assurance 
is imperfect : if the number of instances is practically 
infinite, the assurance is practically complete. Belief 
shades thus from faint presumption, by imperceptible 
increments, into positiveness. When at last we have 
examined all the instances, the induction is complete 
and we know. To quote Mr. Mill: — 

" Induction by simple enumeration — ■ in other words, generali- 
zation of an observed fact from the mere absence of any known 
instance to the contrary — affords in general a precarious and 
unsafe ground of assurance ; for such generalizations are inces- 
santly discovered, on further experience, to be false. Still, how- 
ever, it affords some assurance, sufficient, in many cases, for the 
ordinary guidance of conduct. It would be absurd to say, that 
the generahzations arrived at by mankind in the outset of their 
experience, such as these — food nourishes, fire burns, water 
drowns, — were unworthy of reliance. There is a scale of trust- 
worthiness in the results of the original unscientific induction; and 
on this diversity (as observed in the fourth chapter of the present 

1 Mill's Logic, p. 226. 



Primary Inductions. 21 

book) depend the rules for the improvement of the process. The 
improvement consists in correcting one of these inartificial gener- 
alizations by means of another. As has been already pointed out, 
this is all that art can do. To test a generalization, by showing 
that it follows from or conflicts with some stronger induction, 
some generalization resting on a broader foundation of experience, 
is the beginning and end of the logic of induction." ^ 

Quite a different view from the foregoing has, how- 
ever, been often taken. The name induction has been 
denied to the generalization of experience, and has 
been reserved exclusively for statements in regard to 
the unobserved. Professor Bain speaks as follows : — 

" Induction is the arriving at General Propositions, by m.eans of 
Observation or Fact. 

" In an induction there are three essentials: (i) the result must 
be a proposition — an affirmation of concurrence or non-concur- 
rence — as opposed to a Notion; (2) the Proposition must be 
general^ or applicable to all cases of a given kind; (3) the method 
must be an appeal to observation of fact. 

" The Propositions established by induction are general. A 
single individual concurrence, as ^ the wind is shaking the tree,' is 
in its statement a proposition, but not an induction. On such 
individual statements we base inductions, but one is not enough. 
If the coincidence recurs, we mark the recurrence; we are affected 
by the shock or flash of identity, a very important step in our 
knowledge. If, pursuing the suggestion, we remark that as often 
as the wind is high, the trees are shaken; that the two things 
have concurred within the whole course of our observation; that 
the same concurrence has been uniform in the observation of all 
other persons whose experience we have been informed of, — we 
are then entitled to make a still wider sweep, and to say, ' every 
time that a high wind has been observed, a waving of the trees 
has also been observed.' 

" Still, with all this multitude and uniformity of observations, 

1 Logic, p. 401. 



22 Inductive Logic. 

there is no proper Induction. What then remains ? The answer 
is, the extension of the concurrence from the observed to the 
unobserved cases — to \\\% future which has not yet come within 
observation, to the past before observation began, to the remote 
where there has been no access to observe. This is the leap, the 
hazard of Induction, which is necessary to complete the process. 
Without this leap our facts are barren; they teach us what has 
been, after the event ; whereas we want knowledge that shall 
instruct us before the event, that shall impart v/hat we have no 
means of observing. A complete induction, then, is a generaliza- 
tion that shall express what is conjoined everywhere, and at all 
times, superseding forever the labor of fresh observation. 

" We thus contrast Induction with that species of ' Induction 
improperly so-called,' where a general statement merely sums up 
the observed particulars. 

^' If, after observing that each one of the planets shines by the 
sun's light, we affirm that ' all the planets shine by the sun's light,' 
we make a general proposition to appearance, but it falls short of 
an induction in the full sense of the term. The general statement 
is merely another way of expressing the particulars; it does not 
advance beyond them. But without such advance there is no real 
inference, no march of information, no addition to our knowledge. 
Induction is the instrument of multiplying and extending knowl- 
edge; it teaches us how, from a few facts observed, to affirm a 
great many that have not been observed. If, from the observa- 
tion of the planets now discovered, we make an assertion respect- 
ing all that have yet to be discovered, we make the leap implied 
in real or inductive inference. If the assertion had been made 
when only six planets were known, actual observation would have 
been the guarantee for those six, induction for the remaining hun- 
dred or upwards. 

" The sole method of attaining Inductive truths being the 
observation and comparison of particulars, the sole evidence for 
such truths is Universal Agreement. 

" A permanent or uniform concurrence can be established, in 
the last resort, only by the observation of its uniformity. That 
unsupported bodies fall to the ground, is a conjunction suggested 
by the observation of mankind, and proved by the unanimity of all 



Primmy Inductions. 23 

observers in all times and places. What is found true, wherever 
we have been able to carry our observations, is to be accepted as 
universally true, until exceptions are discovered. 

" Through this method alone — of Universal Agreement in 
detail — can our most general and fundamental truths be dis- 
covered and proved. It is the only proper inductive jnethodP ^ 

This account of induction cannot be consistently ac- 
cepted. The Professor suggests no criterion by which 
one may know when he is justified in taking the hazard 
of a leap in the dark and making an induction. He 
does not say how many instances must be observed 
before the leap is warranted. If only that part of a 
generalization which refers to the unobserved is 
"induction proper," and if "the only proper inductive 
method is the observation of particulars," and if 
"the sole evidence for such truths is universal agree- 
ment," — it is impossible to see how we can have any 
induction at all. If " a permanent or uniform concur- 
rence can be established in the last resort, only by the 
observation of its uniformity," then it cannot be estab- 
lished by what Professor Bain calls induction ; for 
"proper induction" deals only with the unobserved. 
The puzzle here is simply what grows out of the 
mind's necessary assumption of the continuity of the 
existing order. Of course no one can prove the per- 
manence of a thing by observing it every moment. 
How do I know that the sun does not go out of 
existence whenever I cease to look at it } The answer 
is, that having no reason in experience to think that the 
existing order depends upon my attention, I must assume 
that it does not. The truth is that if, after observing 

1 Logic : Deductive and Inductive, pp. 231, 232, 237. 



24 Inductive Logic. 

that each of the planets shines by the sun's light, we 
affirm that "all the planets shine by the sun's light," 
we take the " hazard " of the continuance of the existing 
order, for we are not at this moment observing them. 

When we say, Salt preserves meat, we are not, 
according to Professor Bain, uttering an induction; 
because the preserved meat is now under our eyes; 
it is only when we say that salt will preserve meat, or 
that salt has preserved meat (referring strictly to the 
unobsei'ved cases in the past), that an induction is made: 
yet this can be established only by " the unanimity of 
all observers," which it is manifestly impossible to 
ascertain, and if it could be ascertained, the assertion 
would at once cease to be an induction (since no longer 
referring to the unobserved and making no addition to 
knowledge) : it would be a mere generalization, an 
"induction improperly so-called." 

It would be impossible to make a catalogue of all of 
the primary inductions held by the mind of a single 
person. They refer to every object and undergo 
constant revision and extension. They are not always, 
nor even usually, in the form of universal truths. That 
three-fifths of the wheat in the state is bad, and that on 
the average ten men in a thousand of a certain class 
die every year, are primary inductions. By combination 
of inductions of small extent, wider ones are. made, and 
a steady advance in generality is the result. It is the 
peculiar glory of modern science to have formulated 
such grand inductions as the law of Inertia, that is, 
that every body continues in its state of rest or motion 
unless acted upon ; the law of the persistence of 
energy; the lav/ of the persistence of matter; the law 



Primary Inductions. 25 

that the will can transform some of the energy of the 
body. These laws generalized into a higher induction 
give us the great law of Causation; namely, that if any 
change occurs in things, the matter, the force, and the 
will concerned, can be found among previously existing 
things. Another generalization is, that as far as man 
can explore, the same order is found existing. So far 
as the sun and stars can be observed, they conform to 
the one existing order. 

How long the existing order will continue, we cannot, 
in any proper sense, be said to know. Reasoning can- 
not make any addition to knowledge. Up to the year 
79 A.D., the volcano of Vesuvius had had, within the 
memory of man, no eruption. Experience seemed to 
have demonstrated that it was safe to live upon its 
slopes ; but the eruption came and proved the contrary. 
Manifestly, those uniformities which depend upon the 
co-operation of a number of causes are less stable than 
those which are simpler. Nothing is simpler than the 
law of gravitation; hence such a uniformity as the 
rising and setting of the sun is relied upon with vastly 
more faith than is the quiescence of a volcano. But 
that is only a matter of degree. 

Mr. Mill has made a distinction between Empirical 
Laws and Ultimate Laws. "An empirical law is an 
observed uniformity, presumed to be resolvable into 
simpler laws, but not yet resolved into them." The 
distinction is simple enough in thought, but in practice 
it is impossible to draw the line. 

It may be well, in closing this chapter, to say a few 
words upon the curious popular misunderstanding of 
the maxim that "The exception proves the rule." 



26 Inductive Logic. 

When one has laid down with positiveness some sup- 
posed general principle, and his attention is called to a 
fact inconsistent with it, it is not uncommon to hear 
him say, rather triumphantly, " Oh, that is simply the 
exception that proves the rule"; and he seems some- 
how to feel better fortified in his position than before, 
his generalization being now provided with a necessary 
equipment. Even respectable writers fall into this 
absurd mode of speaking. The fallacy consists in 
taking as a principle, valid in the world of facts, what 
has no sense at all except in the world of statements. 
It is taken as if the finding of a black sheep were in 
some way a confirmation of the generalization that all 
sheep are white ; although, of course, every such case 
is just so much disproof. But if some person, a law- 
maker, an expert, or an authority of some sort, in mak- 
ing statements, excepts a person or thing, then it may 
be legitimately inferred that he assumes the rule to be 
the other way. If, for example, one who lives on the 
shore of Lake Erie speaks of a fine day in March with 
surprise, his so speaking is equivalent to testimony that 
bad weather then and there is the rule ; but a chance 
visitor, luckily enjoying bright skies, would not on that 
account more readily assent to the assertion that March 
weather on Lake Erie is generally bad. Those who in 
their youth have been compelled to learn the rules for 
Latin quantity, find it most convenient to remember 
them by the exceptions. Knowing that amicus is given 
as one of the exceptions in its class, I have no difficulty 
in recalling the rule that " Words in -icus shorten the 
penult"; but this proves only the statement of the 
grammarian, nothing more. In short, the word excep- 



Primary hidiictions. ^ 27 

Hon has two senses ; first, it means the act of excepting ; 
secondly, the thing excluded ; the popular fallacy con- 
sists in substituting the second for the first sense, and 
in supposing that the discovery of a few words with long 
i before the termination -cus makes it easier to believe 
that i so situated is generally short ; when in truth the 
proof is wholly in the fact that a competent authority 
has declared these words to be exceptions. 



CHAPTER V. 
SECONDARY INDUCTIONS. 

Having by the slow, and often tedious, process of 
observing many particulars, established our primary 
inductions, we are prepared to advance with ease and 
rapidity in the making of Secondary Inductions. A 
primary induction, we have learned, is a generalization 
of experience, a truth established by repeated observa- 
tions. A Secondary Induction is the conclusion of a 
syllogism of which one premise is a primary induction, 
and the other premise is the statement of an observed 
fact. When, for example, it has once been admitted, 
as a primary induction, that specific gravities are con- 
stant, a single experiment upon a newly discovered 
metal is sufficient to establish its specific gravity to the 
satisfaction of the scientific world. The single observa- 
tion is combined deductively with the primary induction, 
thus : — 

All specific gravities are constant ; 

The specific gravity of this piece of Rubidium is 1.5; 

Therefore, the specific gravity of Rubidium is always 
1.5. 

This illustration shows in an interesting manner how 
induction and deduction are combined. There is dis- 
covery here, but it is not reached by anything peculiar 
in the method of inference ; that is simply deductive. 
But each of the premises records a discovery made by 
observation ; hence the syllogism is inductive. It has 



Secondary Inductions. 29 

been objected to such syllogisms, that the universal 
proposition could not be affirmed unless we already 
knew the conclusion, and that consequently there is 
only an apparent, and not a real advance in knowledge. 
The reply is, that no reasoning can ever make a sub- 
stantial advance in knowledge ; to give knowledge is 
the function of intuition and observation alone. Rea- 
soning can only display explicitly what was already 
involved implicitly. There is, however, in this case 
what comes very near to positive discovery. It has 
appeared in the last chapter that practical certainty is 
reached, regarding many of the uniformities of nature, 
long before all instances have been examined ; indeed, 
from the very character of most uniformities, it is 
impossible that all instances should be examined. We 
become satisfied that all men are mortal, upon knowl- 
edge of what is a very limited part of the experience of 
the race. When, therefore, it is observed that Socrates 
is a man, the conclusion that he is mortal comes very 
near to being a discovery. The fact that Socrates is a 
man is a discovery of observation ; Socrates might be 
the name of a dog or of a ship. This premise brings 
into the syllogism an advance in knowledge. 

In every-day thinking, primary and secondary induc- 
tions are constantly mingled, and almost all of our 
generalizations partake of the nature of both, or are 
proved in both ways. There is, for instance, a perpet- 
ually accumulating mass of experience that lead is 
heavy, that aluminum is light, and so on. Independ- 
ently of anything else, a primary induction can be 
made regarding each one of the metals. But at the 
same time the broader primary induction that specific 



30 Inductive Logic. 

gravities are constant is receiving perpetual confirma- 
tion, so that each ■ single experience with lead or 
aluminum abundantly warrants a secondary induction 
covering the whole existing amount of that metal. 

After observing a thousand uniformities, every one 
perceives that objects and events in this world run in 
lines of similarity ; a strong presumption, therefore, 
arises that any given object is only one of a class. 
Finding several similar things, we combine the observa- 
tion with the previously established generalization that 
several similarities indicate the line of a uniformity, and 
make an induction accordingly. This is what Dr. Fow- 
ler has called ''the mode of generalization natural to 
immature and uninstructed minds"; but in truth it is 
the necessary procedure of all sane minds. The imma- 
turity and inexperience appear in neglecting care in 
determining the exact course and limits of the lines of 
uniformity. 

Archbishop Whately regarded the uniformity of the 
course of nature as the ultimate major premise in all 
inductions. That is, he did not provide for any primary 
inductions at all. But the uniformity of nature is too 
vast and indefinite an induction for immediate use, even 
in most cases of secondary induction. The doctrine 
does not mean that all objects are alike, and all events 
alike ; it only means that all particular lines of uni- 
formity persist. What these lines are, must be deter- 
mined simply by accumulating instances and making 
generalizations. We must have observed a number of 
lines of particular uniformity, before we could ascend to 
the induction of the general uniformity of nature. To 
quote Mr. Mill: — 



Secondary Inductions. 31 

" But though it is a condition of the validity of every induction 
that there be uniformity in the course of nature, it is not a neces- 
sary condition that the uniformity should pervade all nature. It 
is enough that it pervades the particular class of phenomena to 
which the induction relates. An induction concerning the motions 
of the planets, or the properties of the magnet, would not be 
vitiated though we were to suppose that wind and weather are the 
sport of chance, provided it be assumed that astronomical and 
magnetic phenomena are under the dominion of general laws. 
Otherwise the early experience of mankind would have rested on a 
very weak foundation ; for in the infancy of science it could not 
be known that all phenomena are regular in their course." ^ 

The strangest fact in the history of inductive science 
is that writers have never distinctly recognized and 
stated the fundamental differences of the three great 
classes of inductions, but have persisted in attempting 
to make one comprehensive definition for all, as if the 
process of induction were always precisely the same 
thing. Thus Whately provides only for secondary 
inductions ; Bain, only for primary ones ; Minto and 
Davis, only for such secondary ones as fall under the 
primary induction of causation, which is but a fraction 
of the field of experience. Mr. Mill has thrown so 
much light upon the whole subject, and has made so 
many just discriminations, that it is all the more sur- 
prising that he has not gone a step farther. He says : — 

"Whatever be the most proper mode of expressing it, the 
proposition that the course of nature is uniform, is the funda- 
mental principle, or general axiom of Induction. It would yet be 
a great error to offer this large generaHzation as any explanation 
of the inductive process. On the contrary, I hold it to be itself 
an instance of induction, and induction by no means of the most 
obvious kind. Far from being the first induction we make, it is 

1 Logic, p. 225, note. 



32 Inductive Logic. 

one of the last, or at all events one of those which are latest in 
attaining strict philosophical accuracy. As a general maxim, 
indeed, it has scarcely entered into the minds of any but philoso- 
phers ; nor even by them, as we shall have many opportunities of 
remarking, have its extent and limits been always very justly con- 
ceived. The truth is, that this great generalization is itself founded 
on prior generalizations. The obscurer laws of nature were dis- 
covered by means of it, but the more obvious ones must have been 
understood and assented to as general truths before it was ever 
heard of. We should never have thought of affirming that all 
phenomena take place according to general laws, if we had not 
first arrived, in the case of a. multitude of phenomena, at some 
knowledge of the laws themselves ; which could be done no other- 
wise than by induction. In what sense, then, can a principle, 
which is so far from being our earliest induction, be regarded as 
our warrant for all the others ? In the only sense in which (as 
we have already seen) the general propositions which we place at 
the head of our reasonings when we throw them into syllogisms, 
ever really contribute to their validity. As Archbishop Whately 
remarks, every induction is a syllogism with the major premise 
suppressed ; or (as I prefer expressing it) every induction may be 
thrown into the form of a syllogism by supplying a major premise. 
If this be actually done, the principle which we are now consider- 
ing, that of the uniformity of the course of nature, will appear as 
the ultimate major premise of air inductions, and will, therefore, 
stand to all inductions in the relation in which, as has been shown 
at so much length, the major proposition of a syllogism always 
stands to the conclusion ; not contributing at all to prove it, but 
being a necessary condition of its being proved ; since no conclu- 
sion is proven, for which there cannot be found a true major 
premise." 1 

In this passage the characteristic peculiarities of Mr. 
Mill's mind appear; he tells the truth most clearly, but 
at the same time contradicts and obscures it. If the 
uniformity of nature is a discovery of induction it cannot 

1 Logic, p. 224. 



Secondary Inductions. 33 

be the fundamental principle of induction. We cannot 
lift ourselves over the fence by our own boot-straps. 
Primary inductions are but generalizations and need no 
major premise; for they cannot be thrown into syllo- 
gistic form. Secondary inductions have for their 
major premises the particular uniformities which are 
proximate. We cannot take the uniformity of nature 
as a major premise, and making a single observation, 
proceed at once to a secondary induction, reasoning, 
This object is mortal ; But since nature is uniform ; All 
objects are mortal. The uniformity of nature is a 
generalization only regarding uniformities ; to use it at 
all we must, by accumulating particulars, ascertain the 
existence of a uniformity. And then we can reason. 
All uniformities persist ; This is a uniformity ; There- 
fore it will persist. The only inference that can be 
drawn from the uniformity of nature is the persistence 
of a newly discovered uniformity. 
Professor Minto says: — 

" In his antagonism to a supposed doctrine that all reasoning is 
from general to particular, Mill maintained simpliciter that all 
reasoning is from particulars to particulars. Now, this is true 
only secundum quid, and although, in the course of his argument, 
Mill introduced the necessary qualifications, the unqualified thesis 
was confusing. It is perfectly true that we may infer — we can 
hardly be said to reason — from observed particulars to unob- 
served. We may infer, and infer correctly, from a single case. 
The village matron, called in to prescribe for a neighbor's sick 
child, infers that what cured her own child will cure the neigh- 
bor's, and prescribes accordingly. And she may be right. But 
it is also true that she may be wrong, and that no fallacy is more 
common than reasoning from particulars to particulars without the 
requisite precautions." ^ 

1 Logic, p. 266. 



34 Inductive Logic. 

We cannot admit that there is any such thing as 
inferring, or reasoning, from one particular to another. 
The village matron does not infer from her child to the 
neighbor's grindstone or barn-door, and the fact that 
she does not is proof that she does not take particulars 
at random. Her process of thought is this : These two 
particulars (the children) belong to the same natural 
kind ; Things of the same natural kind are similarly 
affected by the same thing ; This medicine cured my 
child; Therefore, it will cure this one. The matron's 
reasoning is syllogistic throughout ; if she makes an 
error it is simply in observation as to whether the 
medicine did cure her own child, or as to whether the 
neighbor's child is in the same physical condition. 
The matron proceeds from primary inductions through 
particular observations to secondary inductions. The 
"requisite precautions" always include attention to 
these steps. 

In the first edition of his Logic, Mr. Mill said: — 

" The induction by which they [the mathematical axioms and 
the law of causation] are established is of that kind which can 
establish nothing but empirical laws; an empirical law, however, 
of which the truth is exemplified at every moment of time and in 
every variety of place or circumstance, has an evidence which sur- 
passes that of the most rigid induction, even if the foundation of 
scientific induction were not itself laid (as we have seen that it is) 
in a generalization of this very description." ^ 

In this remarkable passage, it was assumed that only 
secondary inductions are scientific inductions, and yet 
it was affirmed that they are based upon the primary, 

1 Page 340. 



Secondary Inductions. 35 

and that the primary are so firm that they would sur- 
pass the secondary, were it not that the secondary, 
being based upon them, must be exactly as strong. It 
is true that in the eighth, the last, edition of the Logic 
this passage is omitted; but the confusion of thought 
still attaches to Mr. Mill's doctrine, and appears in the 
books which, like Dr. Fowler's, are based upon his 
earlier editions. Mr. Mill's contention amounts simply 
to this, that a secondary induction made from one clear 
case in combination with one of our broadest primary 
inductions (say the law of causation), is far more trust- 
worthy than a new primary induction made independ- 
ently regarding a limited class of phenomena. And 
this is undoubtedly true. 



CHAPTER VI. 



MIXED INDUCTIONS. 



We know by intuition that if certain things are true, 
certain other things are also true. When, therefore, 
one of these facts of the first class has been estab- 
lished by observation, one of the facts of the second 
class can be established by making a syllogism, of 
which one premise is known to be true by intuition, 
and the other by observation; the conclusion will be a 
Mixed Induction. 

We know, mathematically, that if the surface of the 
sea is not flat, but curved, the masts of ships must 
appear before their hulls. We observe that the masts 
do actually appear first. The conclusion, that the sur- 
face of the sea is curved, is a mixed induction. 

The nature of mixed inductions is well illustrated in 
the famous discoveries of Sir Isaac Newton. We quote 
from Mr. Mill : — 

" Newton began by an assumption, that the force which at each 
instant deflects a planet from its rectilineal course, and makes it 
describe a curve round the sun, is a force tending directly towards 
the sun. He then proved that, if it be so, the planet will describe, 
as we know by Kepler's first law it does describe, equal areas in 
equal times; and, lastly, he proved that if the force acted in any 
other direction whatever, the planet would not describe equal areas 
in equal times. It being thus shown that no other hypothesis 
could accord with the facts, the assumption was proved; the 
hypothesis became a law, established by the method of difference. 
Not only did Newton ascertain by this hypothetical process the 



Mixed Inductions. 37 

direction of the deflecting force ; he proceeded in exactly the same 
manner to ascertain the law of variation of the quantity of that 
force. He assumed that the force varied inversely as the square 
of the distance ; showed that from this assumption the remaining 
two of Kepler's laws might be deduced; and, finally, that any 
other law of variation would give results inconsistent with those 
laws, and inconsistent, therefore, with the real motions of the planets, 
of which Kepler's laws were known to be a correct expression." ^ 

That is, Newton showed mathematically that if the 
planets move in a given manner, they must be affected 
by a force acting toward the sun and varying inversely 
as the square of the distance; Kepler had shown that 
the planets do move in the given manner; the mixed 
induction was therefore established that there is such a 
force. 

It will be seen that Mr. Mill introduces this as an 
example of hypothesis, but it will also be seen that it 
was wholly unnecessary for Newton to make any con- 
jecture or assumption. All he had to do was to ask. 
The motions being as they are observed to be, what, 
mathematically, must be the direction and law of the 
force } It is not necessary to form an hypothesis that 
the surface of the sea is curved and then test that 
hypothesis by looking at an incoming ship. All that 
is necessary is to state the mathematical possibilities 
and then observe the facts; the conclusion follows of 
course. 

We take another fine illustration from Sir John 
Herschel : — 

" It had been objected to the doctrine of Copernicus, that, were 
it true, Venus (and, it might have been added. Mercury, as the 
other inferior planet) should appear sometimes horned like the 

1 Logic, p. 351. 



38 Inductive Logic. 

moon. To this he answered by admitting the conclusion, and 
averring that, should we ever be able to see its actual shape, it 
would appear so. It is easy to imagine with what force the 
application would strike every mind when the telescope confirmed 
this prediction, and showed the planet just as both the philosopher 
and his objectors had agreed it ought to appear." ^ 

Having considered the three kinds of induction, we 
are now ready to answer several questions proposed by 
Mr. Mill: — 

"In order to a better understanding of the problem which 
the logician must solve if he would establish a scientific theory of 
induction, let us compare a few cases of incorrect inductions with 
others which are acknowledged to be legitimate. Some, we know, 
which were believed for centuries to be correct, were, nevertheless, 
incorrect. That all swans are white, cannot have been a good 
induction, since the conclusion has turned out to be erroneous. 
The experience, however, on which the conclusion rested was 
genuine. From the earliest records, the testimony of all the 
inhabitants of the known world was unanimous on the point. The 
uniform experience of the inhabitants of the known world, agree- 
ing in a common result, is not always sufficient to establish a 
general conclusion. . . . When a chemist announces the existence 
and properties of a newly discovered substance, if we confide in 
his accuracy, we feel assured that the conclusions he has arrived 
at will hold universally, although the induction be founded but on 
a single instance. We do not withhold our assent, waiting for a 
repetition of the experiment; or if we do, it is from a doubt 
whether the one experiment was properly made, not whether, if 
properly made, it would be conclusive. Here, then, is a general 
law of nature, inferred without hesitation from a single instance; 
an universal proposition from a singular one. Now, mark another 
case and contrast it with this. Not all the instances which have 
been observed since the beginning of the world, in support of the 
general proposition that all crows are black, would be deemed a 
sufiicient presumption of the truth of the proposition, to outweigh 

1 Discoicrse on the Study of N'atural Philosophy, § 299. 



Mixed Inductions. 39 

the testimony of one unexceptionable witness who should affirm 
that in some region of the earth not fully explored, he had caught 
and examined a crow, and had found it to be gray. 

" Why is a single instance, in some cases, sufficient for a com- 
plete induction, while in others, myriads of concurring instances, 
without a single exception known or presumed, go such a very 
little way towards establishing an universal proposition? Who- 
ever can answer this question knows more of the philosophy of 
logic than the wisest of the ancients, and has solved the great 
problem of induction." ^ 

Our discussion up to this point has prepared the 
student to ansv^er Mr. Mill's question, and to claim the 
proud distinction of " knowing more of the philosophy 
of logic than the wisest of the ancients." It is plain 
that when a chemist determines for the first time the 
specific gravity of a new substance, rubidium, for exam- 
ple, he combines this one observation deductively with 
the acknowledged primary induction that chemical and 
physical properties of the several natural kinds are 
constant, and thus reaches at once the secondary induc- 
tion, that the specific gravity of rubidium will be always 
found 1.5, or whatever the determination may be. 
Whenever a single instance leads to an induction, it 
is a secondary induction or a mixed induction. Bacon 
called such instances "crucial instances," from the 
Latin crux, a finger-post ; since they point out the line 
of uniformity. No single instance can give a primary 
induction. In investigating the color of swans and 
crows we start with the well-established primary induc- 
tion that color is, in animals, an uncertain quality. 
Combining this with the observation that these crows 
are black, we, of course, reach no conclusion. We have, 

1 Logic, p. 227. 



40 Inductive Logic. 

however, made a primary induction that all English 
crows are black ; and this is correct. This leads us to 
remark that, in making an induction, it is necessary to 
define correctly the field under investigation. Having 
seen a thousand Chinamen in California, we conclude 
by induction that all Chinamen are, on the average, 
shorter than Americans. But when we learn that these 
men all came from one province, that of which Hong- 
Kong is the port, we change, not the induction, but 
the area of it ; it concerns not Chinamen but one sort 
of Chinamen. So the induction "All crows are black" 
was correct for England, but not certainly for the whole 
world. 



CHAPTER VII. 
FACTS OF RESEMBLANCE. 

The earliest activities of the infant mind must be in 
observing single facts. But there is one recurring fact 
of relation which must soon force itself upon the atten- 
tion ; this is the resemblance between many of these 
single facts. As we say, in popular language, the same 
phenomenon is repeated. The word same thus used 
means merely that a resembling phenomenon comes. 
Meeting a multitude of similar phenomena, the mind at 
length forms a general concept, and finally invents a 
name which we call a common noun, as mmi or tree. 
The existence of such words depends upon the fact of 
the existence of numbers of objects recognized by the 
mind as similar. 

And not only do objects resemble one another, but the 
changes and states of objects have also resemblances. 
The universe is perceived to be full of lines of resem- 
blance or, to use a more common term. Uniformity. 
The phenomena about us at this moment are like 
the phenomena of yesterday and of a year ago to-day. 
" That which hath been is that which shall be ; and that 
which hath been done is that which shall be done : and 
there is no new thing under the sun. Is there a thing 
whereof men say. See, this is nev/.? it hath been already, 
in the ages which were before us." ^ As previously 
remarked, a universe in which every object should be 

1 Ecclesiastes, i. 9, 10. 



42 Inductive Logic. 

unique and every event a surprising novelty is perfectly 
conceivable ; the conception contradicts no law of 
thought or, so far as we know, of being. But such is 
not the universe in which we live. 

As one who enters, for example, a large store of 
pottery, soon discovers that much of the stock is in 
lots, and that this cup is like other cups, and that 
platter like other platters, so the observer of nature 
perceives that things are in lots and are passing through 
similar changes. 

The possibility of language rests upon the recurrence 
of resemblances. Not only are objects alike, but their 
changes and relations are alike. The words used to 
describe the phenomena of yesterday are appropriate 
to-day. Nature may be divided into groups of similari- 
ties ; and the phrase " Uniformity of Nature " embodies 
the opinion that things remain essentially similar to 
themselves, and of course, therefore, similar to the 
other things which at any time resemble them. Our 
belief in the uniformity of nature is the belief that the 
quantities and qualities of matter and force, and the 
faculties of mind, remain as they are. The integrity of 
the existing order is unimpaired. 

Long inductive arguments may be constructed by 
successive judgments of resemblance, the intuitively 
known axiom that things that are equal to the same 
thing are equal to each other being the general major 
premise. These arguments are therefore mixed induc- 
tions. We will add two examples, one from the science 
of language and one from the science of geology. 

The following analysis of an inductive argument is 
taken from Fowler's Inductive Logic. — 



Facts of Re setnb lance. 43 

" The Method of Concomitant Variations is that which is most 
frequently employed in the Science of Language. It is found, for 
instance, that between two dissimilar words employed at different 
epochs to express the same idea may be interpolated a number of 
intermediate forms employed at intermediate epochs, which make 
the transition gradual and natural. From this circumstance it is 
inferred that the word used at the later epoch is derived from that 
used at the earlier epoch, certain tendencies of speech being regarded 
as the cause of the divergence. ' Thus, at first sight,' says M. 
Brachet, ' it is hard to see that djne is derived from animaj but 
history, our guiding-line, shows us that in the thirteenth century 
the word was written anine^ in the eleventh aneme^ in the tenth 
anime^ which leads us straight to the Latin anijna.'' In this case 
there can be no doubt of the truth of the conclusion." ^ 

This analysis we cannot at all accept. The proof 
that ante is the same as anima is based upon a number 
of successive observations of facts of resemblance. 
Anima and anime are so much alike in look, sound, and 
meaning, that we pronounce them the same ; this is 
true also of anime and ane7ne, of aneme and anme, of 
anme and dme. We therefore construct the equation 

anima = dnime = aneme = anme = dme. 
.'. ani^na ^=dme. 

There is positively nothing here that varies concom- 
itantly with the word anima. The explanation that 
" certain tendencies of speech are the cause of the 
divergence" is just like the explanation that opium 
causes sleep because "it has a soporific quality"; it 
explains nothing. The method generally employed in 
philological investigations is that of direct observation 
of resemblances. The proposition that anima and d^ne 
are the same word is an induction, because it is the 

1 Page 200. 



44 Inductive Logic. 

statement of a fact not directly observable and the 

statement is based upon observations. It is really a 

mixed induction ; for it rests upon the axiom that 

things that are equal to the same thing are equal to 
each other. 

Let us try to analyze the following argument for 
the evolution of the horse, taken from Le Conte's 
Geology : — 

" Genesis of the Horse. — In conclusion, it will be interesting 
and instructive to run out one of these branches and show in more 
detail the genesis of one of the extreme forms. For this purpose 
we select the Horse, because it has been somewhat accurately 
traced by Huxley and by Marsh. About thirty-five or forty 
species of this family, ranging from the earliest Eocene to the 
Quaternary, are known in the United States. The steps of evo- 
lution may therefore be clearly traced. 

"In the lower part of the Eocene basin {Coryphodon beds') of 
Green River is found the earliest known animal in the direct line 
of descent of the horse family, viz., the recently described 
Eohippus of Marsh. This animal had three toes on the hind-foot 
and four perfect, serviceable toes on the fore-foot ; but, in addi- 
tion, on the fore-foot an imperfect fifth metacarpal (spHnt), and 
possibly a corresponding rudimentary fifth toe (the thumb), like a 
dew-claw. Also, the two bones of the leg and fore-arm were yet 
entirely distinct. This animal was no larger than a fox. Next, 
in the Middle Eocene (Bridger beds), came the Orohippiis of 
Marsh, an animal of similar size, and having similar structure, 
except that the rudimentary thumb or dew-claw is dropped, leav- 
ing only four toes on the fore-foot. Next came, in the Lower 
Miocene., the Mesohipptis., in which the fourth toe has become a 
rudimentary and useless splint. Next came, still in the Miocene., 
the Miohippus of the United States and nearly allied Anchithere 
of Europe, more horse-like than the preceding. The rudimentary 
fourth spHnt is now almost gone, and the middle hoof has become 
larger ; nevertheless, the two side-hoofs are still serviceable. The 
two bones of the leg have also become united, though still quite 



Facts of Resemblance. 45 

distinct. T\As 2si\v[v3\^N2.'s> 2^ovi\. the size of a sheep. Next came, 
in the Upper Miocene, and Lower Pliocene, the Protohippus of 
the United States and allied Hipparion of Europe, an animal 
still more horse-like than the preceding, both in structure and 
size. Every remnant of the fourth spHnt is now gone ; the middle 
hoof has become still larger, and the two side-hoofs smaller and 
shorter, and no longer serviceable, except in marshy ground. It 
was about the size of the ass. Next came, in the Plioceiie, the 
Pliohippiis, almost a complete horse. The hoofs are reduced to 
one, but the splints of the two side-hoofs remain to attest the line 
of descent. It differs from the true horse in the skull, shape of 
the hoof, the less length of the molars, and some other less im- 
portant details. Last comes, in the Quaternary, the modern 
horse — Eqtius. The hoof becomes rounder, the splint-bones 
shorter, the molars longer, the second bone of the leg more rudi- 
mentary, and the evolutionary change is complete. 

" Similar gradual changes, becoming more and more horse-like, 
may be traced in the shape of the head and neck, and especially 
in the gradually increasing length and complexity of structure of 
the grinding teeth." 

"There can be no doubt that if we could trace the line of 
descent still further back we would find a perfect five-toed an- 
cestor. From this normal number of five, the toes have been 
successively dropped, according to a regular law. In the Perisso- 
dactyl line first the thumb. No. i, was dropped; then the little 
finger, No. 5 ; then the first and ring-fingers, Nos. 2 and 4, were 
shortened up more and more and finally disappeared, and only the 
middle finger, No. 3, remained in the modern horse. In the 
Artiodactyl line, after the dropping of No. i, then Nos. 2 and 5 
of the four-toed foot were shortened and gradually disappeared, 
and Nos. 3 and 4 remained in the Ruminants. " 

" From the earliest and most generalized types, therefore, to 
the present specialized types, the principal changes have been, 
first, from plantigrade to digitigrade; second, from short-footed 
digitigrade to long-footed digitigrade, i.e., increasing elevation of 
the heel; third, from five toes to one toe in the Horse, or two toes 
in Ruminants ; and, fourth, from simple omnivorous molars to the 
complex herbivorous mill-stones of the Horse and the Ox. 



4-6 Inductive Logic. 

"The change from plantigrade to digitigrade, with increasing 
elevation of the heel, when taken in connection with increasing 
size of the brain, and therefore presumably with increasing brain- 
power, shows a gradual improvement of structure adapted for 
speed and activity, and a pari-passu increase of nervous and 
muscular energy necessary to work the improved structure." ^ 

The foregoing argument is just like that regarding 
the words dme and a7iima ; Eohippus so closely resem- 
bles OrohippiLS that they must be the same ; Orohippus 
must be the same as Mesohippus ; Mesohippus must be 
the same as Protohippus; Protohippus is the same as 
Pliohippus ; Pliohipptts is the same as E quits ; there- 
fore the modern horse is the same as the Eohippus. 
The force of this argument will depend upon the 
strength of the impressions of resemblance made upon 
various minds. Professor Huxley regarded it as 
demonstrative. 

1 Pages 540-543- 



CHAPTER VIII. 
FACTS OF COEXISTENCE. 

Every observer very quickly perceives that the various 
objects in the world may be divided into groups of 
permanent coexistences. Here is a mass of matter 
with specific gravity 19.34, a yellow color, malleable, 
ductile, etc., and there is another mass of matter in 
which the same phenomena coexist, and there is an- 
other. We call all these masses gold; and we say 
that gold is a kind of matter. Malleability, ductility, 
etc., are commonly called the properties of gold. But 
in truth we know absolutely nothing about gold except 
these properties. The weight does not possess the 
ductility, nor does the color possess the malleability; 
but the coexistence of all these phenomena is gold. 

No approach has been made by science to any reason 
why certain phenomena permanently coexist ; as, for 
instance, why the metal whose specific gravity is 19.34 
should be yellow, and the metal whose specific gravity 
is 10.5 should be white. It is easy to say that all the 
properties probably depend upon some common fact of 
causation ; but in the present state of science such a 
remark has no meaninsr. 

A very large part of the work of science is in ascer- 
taining the various natural kinds of objects. Mr. Mill 
magnifies the notion of cause and calls it " the root of 
the whole theory of induction." But it is plain that the 
notion of coexistence is an equally important root. 



48 Inductive Logic. 

We cannot reason that such and such things must 
coexist; we can only discover that they do. This 
work has nothing to do with causation. It has nothing 
to do with the unknown. It does not proceed by in- 
ference. It is the orderly arrangement of what we 
know. 

One vast attempt of Induction is to classify the 
objects in nature, that is, to discover and define all 
natural kinds. In this attempt it is soon perceived 
that there are groups within groups. Vegetables, for 
example, are a natural kind ; but the vegetable king- 
dom may be subdivided into more limited kinds, and 
these kinds may be again subdivided. 

A distinction is made between Natural and Artificial 
kinds. We may, for temporary convenience, divide 
objects according to some one property, as yellowness. 
And then gold and oranges and salmon will be of the 
same kind. Such a group is called an Artificial Kind. 
But Natural Kinds are so called because the objects 
which compose them resemble each other in a multi- 
tude of characteristics and appear, in fact, grouped 
together by nature. The great botanist Linnaeus 
systematized plants according to the numbers of sta- 
mens and pistils, neglecting other features. This was 
a convenient, but highly artificial, arrangement; since 
it brought into the same order plants on the whole 
utterly diverse. Modern botany takes into considera- 
tion a multitude of particulars in stem, leaf, flower, and 
fruit; and so reaches a natural system. No classifica- 
tion is natural which depends in the least degree upon 
the caprice of the investigator; it must force itself 
upon all observers as existing in nature. 



Facts of Coexistence. 49 

That there is a kind of objects which we may call 
plants and another kind of objects which we may call 
animals is generally admitted. But when we come to 
subdivide the animal and vegetable kingdoms, differ- 
ences of opinion arise. It is obvious that certain 
individuals greatly resemble one another; they con- 
stitute natural groups, which may be called species. 
Certain species resemble one another ; they may be 
associated in larger groups and called genera. So the 
genera may be grouped into orders, and the orders into 
classes. 

Philosophers have discussed the question whether 
there is a point where natural subdivision ends. If 
there is such a point, then one of the smallest possible 
natural groups would be called an iiifima species. If, 
on the other hand, there be a group which cannot 
naturally be included in a larger, such a group would 
be called a summu7n gemts. 

The most interesting question in modern natural 
science is, whether the various natural groups of ani- 
mals and plants — species, genera, orders, etc. — are 
naturally separated by distinct lines. The discussion 
has taken the form of an inquiry into the true nature 
of species. The main points in it can be conveniently 
presented in the words of Professor Asa Gray : — 

"The ordinary and generally received view assumes the inde- 
pendent, specific creation of each kind of plant and animal in a 
primitive stock, which reproduces its like from generation to gen- 
eration, and so continues the species. Taking the idea of species 
from this perennial succession of essentially similar individuals, the 
chain is logically traceable back to a local origin in a single stock, 
a single pair, or a single individual, from which all the individuals 



50 Inductive Logic. 

composing the species have proceeded by natural generation. 
Although the similarity of progeny to parent is fundamental in the 
conception of species, yet the likeness is by no means absolute ; 
all species vary more or less, and some vary remarkably — partly 
from the influence of altered circumstances, and partly (and more 
really) from unknown constitutional causes which altered condi- 
tions favor rather than originate. But these variations are sup- 
posed to be mere oscillations from a normal state, and in Nature 
to be limited if not transitory ; so that the primordial differences 
between species and species at their beginning have not been 
effaced, nor largely obscured, by blending through variation. 
Consequently, whenever two reputed species are found to blend in 
Nature through a series of intermediate forms, community of origin 
is inferred, and all the forms, however diverse, are held to belong 
to one species. Moreover, since bisexuality is the rule in Nature 
(which is practically carried out, in the long run, far more gener- 
ally than has been suspected), and the heritable qualities of two 
distinct individuals are mingled in the offspring, it is supposed that 
the general sterility of hybrid progeny interposes an effectual bar- 
rier against the blending of the original species by crossing. 

" From this generally accepted view the well-known theory of 
Agassiz, and the recent one of Darwin, diverge in exactly opposite 
directions. 

" That of Agassiz differs fundamentally from the ordinary view 
only in this, that it discards the idea of a common descent as the 
real bond of union among the individuals of a species, and also 
the idea of a local origin — supposing, instead, that each species 
originated simultaneously, generally speaking, over the whole 
geographical area it now occupies, or has occupied, and in per- 
haps as many individuals as it numbered at any subsequent 
period. 

" Mr. Darwin, on the other hand, holds the orthodox view of 
the descent of all the individuals of a species not only from a local 
birthplace, but from a single ancestor or pair ; and that each 
species has extended and established itself, through natural agen- 
cies, wherever it could ; so that the actual geographical distribu- 
tion of any species is by no means a primordial arrangement, but 
a natural result. He goes farther, and this volume \The Origin 



Facts of Coexistence. 51 

of S;pecies'\ is a protracted argument intended to prove that the 
species we recognize have not been independently created as such, 
but have descended, Uke varieties, from other species. Varieties, 
on this view, are incipient or possible species ; species are varie- 
ties of a larger growth, and a wider and earlier divergence from 
the parent stalk ; the difference is one of degree, and not of kind."i 

"In applying his principle of natural selection to the work in 
hand, Mr. Darwin assumes, as we have seen : (i) Some variability 
of animals and plants in nature ; (2) the absence of any definite 
distinction between slight variations and varieties of the highest 
grade ; (3) the fact that naturalists do not practically agree, and 
do not increasingly tend to agree, as to what forms are species and 
what are strong varieties, thus rendering it probable that there may 
be no essential and original difference, or no possibility of ascer- 
taining it, at least in many cases ; also (4) that the most flourish- 
ing and dominant species of the larger genera on an average vary 
most (a proposition which can be substantiated only by extensive 
comparisons, the details of which are not given); and (5) that in 
large genera the species are apt to be closely but unequally allied 
together, forming little clusters round certain species — just such 
clusters as would be formed if we suppose their members once to 
have been satellites or varieties of a central or parent species, but 
to have attained at length a wider divergence and a specific 
character. The fact of such association is undeniable ; and the 
use which Mr. Darwin makes of it seems fair and natural. 

" The gist of Mr. Darwin's work is to show that such varieties 
are gradually diverged into species and genera through natural 
selection ; that natural selection is the inevitable resul* oi the 
struggle for existence which all living things are engaged in ; and 
that this struggle is an unavoidable consequence of several natural 
causes, but mainly of the high rate at which all organic beings 
tend to increase." ^ 

" Returning for a moment to De Candolle's article, we are dis- 
posed to notice his criticism of Linnaeus's 'definition ' of the term 
species {Philosophia Botanica, No. 157): ^Species tot numerainus 
quot diversae forrnae in principio S7int creatae'' — which he 

^ Darwiniana, p. ii. ^ Ibid., p. 36. 



52 Inductive Logic. 

declares illogical, inapplicable, and the worst that has been pro- 
pounded. ' So, to determine if a form is specific, it is necessary 
to go back to its origin, which is impossible. A definition by a 
character which can never be verified is no definition at all.' 

" Now, as Linnaeus practically applied the idea of species with 
a sagacity which has never been surpassed, and rarely equaled, 
and, indeed, may be said to have fixed its received meaning in 
natural history, it may well be inferred that in the phrase above 
cited he did not so much undertake to frame a logical definition, 
as to set forth the idea which, in his opinion, lay at the foundation 
of species ; on which basis A. L. Jussieu did construct a logical 
definition — 'Nunc rectius definitur perennis individuorum similium 
successio continuata generatione renascentium.' The fundamental 
idea of species, we would still maintain, is that of a chain of which 
genetically connected individuals are the links. That, in the prac- 
tical recognition of species, the essential characteristic has to be 
inferred, is no great objection — the general fact that like engen- 
ders like being an induction from a vast number of instances, and 
the only assumption being that of the uniformity of Nature. The 
idea of gravitation, that of the atomic constitution of matter, and 
the like, equally have to be verified inferentially. If we still hold- 
to the idea of Linnaeus, and of Agassiz, that existing species were 
created independently and essentially all at once at the beginning 
of the present era, we could not better the propositions of Linnaeus 
and of Jussieu. If, on the other hand, the time has come in which 
we may accept, with De Candolle, their successive origination, at 
the commencement of the present era or before, and even by 
derivation from other forms, then the ' /;/ principio ' of Linnaeus 
will refer to that time, whenever it was, and his proposition be as 
sound and wise as ever." ^ 

"... Species, as I have said (in Sillintan''s Journal articles) 
are not facts or things, but judgments, and, of course, fallible 
judgments. How fallible, the working naturalist knows and feels 
more than any one else." ^ 

Inductive Classificatio7i is the orderly arrangement of 
things in their natural groups or kinds. We may 

1 Darwiniana, p. 201. ^ Letters., p. 657. 



Facts of Coexistence. 53 

classify mental states or social movements, as well as 
physical forces and material objects, minerals, plants, 
and animals. 

Nomenclature is a system of names for the various 
things classified. In Botany the name of a plant is 
always in Latin, and consists of the name of the genus, 
followed by the name of the species, as Viola blanda, 
sweet white violet. Unfortunately, no one has yet 
thought of any way of forming botanical names from 
natural characteristics, so that the nomenclature, also, 
may be natural. On the contrary, the names of genera 
and species have been assigned by discoverers for trivial 
and often ridiculous reasons, and the whole scientific 
world has been forced to perpetuate the memory of silly 
caprices. This is an ignominy which no disciplined 
mind can think of without indignation. In Chemistry 
the names of substances are compounded of those of 
their elements, with prefixes and terminations suggest- 
ing their proportions. Chemical nomenclature is the 
best we have, but its development has lagged behind 
the general progress of the science. Mineralogy needs 
nothing more than an adequate nomenclature. A 
system of names suggesting both crystallography and 
chemical composition would be far preferable to smith- 
ite, jonesite, and brownite. 

Terminology is the precise vocabulary used in describ- 
ing the parts, qualities, and actions of the objects of 
science. Botany has a wonderfully copious vocabulary. 
This vocabulary is strictly inductive ; the meaning of 
each word is fixed by direct examination of typical 
specimens. Such words as serrate, dentate, crenate, 
runcinate, bipinnatifid, etc., are defined by exhibiting 



54 Inductive Logic. 

to the learner the parts of plants which they describe, 
and each is ever afterwards used in precisely the same 
sense. By the use of a proper terminology, scientists 
can convey to one another, in a few words, accurate 
descriptions of phenomena, which pages of popular 
phraseology would leave still obscure. 



CHAPTER IX. 

FACTS OF CAUSATION AND FACTS OF 
SUCCESSION. 

It is a matter of observation that things in this 
universe react upon one another. It is further observed 
that after such reactions the things sometimes appear 
in new forms. This property of reacting, or of present- 
ing new forms, is called the power of Causation. The 
several reactions of things are called events. The 
things which react are said to be the causes of these 
events. If things appear in new forms, they are said 
to be, in their antecedent forms, the causes of them- 
selves in their subsequent forms. 

This power of affecting, or being affected, is an 
ultimate property of things. It is one of those ulti- 
mate properties the coexistence of which constitutes 
the existing order. Science never attempts the explana- 
tion of ultimate properties ; or rather, when science 
finds anything inexplicable she calls it ultimate. 

Things exist in space, and events occur in time. 
Time is marked and estimated by the succession of 
events. And these events are seen to have often a 
certain relation to one another. Just as there are cer- 
tain uniform coexistences of phenomena, so there are 
certain uniform successions. Yellowness and ductility 
present themselves simultaneously in gold ; contact 
with red-hot iron and pain in the flesh present them- 



56 Inductive Logic. 

selves as antecedent and consequent events. The 
events of history seem to come in chains, one link 
drawing on the next. So impressed have some philoso- 
phers been with this appearance of concatenation among 
events, that they have attempted to define causation 
itself in terms of succession, and they have thus brought 
great confusion into the science of inductive logic. 

Perhaps it may be easier to define the difficult word 
Cause, and to show the relation of causation and suc- 
cession, in connection with a concrete example. We 
will, therefore, take an instance classic in the history 
of inductive science, one of the experiments of the 
illustrious Count Rumford upon heat. The illustration 
will be useful not only here but in subsequent chapters, 
and it is so interesting that we will give it at length, 
and in the Count's own words. 

" Being engaged lately in superintending the boring of cannon 
in the workshops of the miUtary arsenal at Munich, I was struck 
with the very considerable degree of heat which a brass gun 
acquires, in a short time, in being bored ; and with the still more 
intense heat, much greater than that of boiling water, as I found 
by experiment, of the metallic chips separated from it by the 
borer. From whence comes the heat actually produced in the 
mechanical operation above-mentioned? . . . 

"... Taking a cannon, a brass six-povi,ider, cast solid, and 
rough as it came from the foundry, and fixing it horizontally in 
the machine used for boring, and at the same time finishing the 
outside of the cannon by turning, I caused its extremity to be cut 
off ; and, by turning down the metal in that part, a solid cylinder 
was formed, 7|- inches in diameter, and c)-^^ inches long ; which, 
when finished, remained joined to the rest of the metal, that which, 
properly speaking, constituted the cannon, by a small cylindrical 
neck, only i\ inches in diameter, and 3^^^ inches long. This 
short cylinder, which was supported in its horizontal position, and 



Facts of Catisation and Facts of Succession. 57 

turned round its axis, by means of the neck by which it remained 
united to the cannon, was now bored with the horizontal borer 
used in boring cannon ; but its bore, which was 3.7 inches in 
diameter, instead of being continued through its whole length, 9.8 
inches, was only 7.2 inches in length ; so that a solid bottom 
was left to this hollow cylinder, which bottom was 2.6 inches in 
thickness. 

" The cyhnder being designed for the express purpose of gener- 
ating heat by friction, by having a blunt borer forced against its 
solid bottom at the same time that it should be turned round its 
axis by the force of horses, in order that the heat accumulated in 
the cylinder might from time to time be measured, a small round 
hole, 0.37 of an inch only in diameter, and 4.2 inches in depth, for 
the purpose of introducing a small cylindrical mercurial thermom- 
eter, was made in it, on one side, in a direction perpendicular to 
the axis of the cylinder, and ending in the middle of the solid 
part of the metal which formed the bottom of its bore. 

^^ Exper. J. — A quadrangular oblong deal box, water-tight, 
iii English inches long, 9^^ inches wide, and 9^^^ inches deep, 
being provided, with holes or slits in the middle of each of its 
ends, just large enough to receive, the one, the square iron rod to 
the end of which the blunt steel borer was fastened, the other, the 
small cylindrical neck which joined the hollow cylinder to the 
cannon ; when this box was put into its place it was fixed to the 
machinery, in such a manner that its bottom being in the plane of 
the horizon, its axis coincided with the axis of the hollow metallic 
cylinder ; it is evident, from the description, that the hollow 
metallic cylinder would occupy the middle of the box, without 
touching it on either side ; and that, on pouring water into the 
box, and filling it to the brim, the cyhnder would be completely 
covered, and surrounded on every side, by that fluid. And further, 
as the box was held fast by the strong square iron rod which 
passed, in a square hole, in the centre of one of its ends, while the 
round or cylindrical neck, which joined the hollow cylinder to the 
end of the cannon, could turn round freely on its axis in the round 
hole in the centre of the other end of it, it is evident that the 
machinery could be put in motion, without the least danger of 
forcing the box out of its place, throwing the water out of it, or 



58 Inductive Logic. 

deranging any part of the apparatus. Everything being ready, I 
proceeded to make the experiment I had projected, in the follow- 
ing manner. 

" The hollow cylinder having been previously cleaned out, and 
the inside of its bore wiped with a clean towel till it was quite dry, 
the square iron bar, with the blunt steel borer fixed to the end of 
it, was put into its place ; the mouth of the bore of the cylinder 
being closed at the same time, by means of the circular piston, 
through the centre of which the iron bar passed. The box was 
then put in its place, and the joinings of the iron rod, and of the 
neck of the cylinder, with the two ends of the box, having been 
made water-tight by means of collars of oiled leather, the box was 
filled with cold water (viz., at the temperature of (id^^, and the 
machine was put in motion. The result of this beautiful experi- 
ment was very striking, and the pleasure it afforded me amply 
repaid me for all the trouble I had had, in contriving and arrang- 
ing the complicated machinery used in making it. The cylinder, 
revolving at the rate of about 32 times in a minute, had been in 
motion but a short time, when I perceived, by putting my hand 
into the water, touching the outside of the cylinder, that heat was 
generated ; and it was not long before the water which surrounded 
the cylinder began to be sensibly warm. At the end of i hour, 

1 found, by plunging a thermometer into the water in the box (the 
quantity of which fluid amounted to 18.77 lb. avoirdupois, or 2.\ 
wine gallons), that its temperature had been raised no less than 
47 degrees, being now 107° of Fahrenheit's scale. When 30 
minutes more had elapsed, or i hour and 30 minutes after the 
machinery had been put in motion, the heat of the water in the 
box was 142°. At the end of 2 hours, reckoning from the begin- 
ning of the experiment, the temperature of the water was found to 
be raised to 178°. At 2 hours 20 minutes it was at 200°; and at 

2 hours 30 minutes it actually boiled. 

" It would be difficult to describe the surprise and astonishment 
expressed in the countenances of the by-standers, on seeing so 
large a quantity of cold water heated, and actually made to boil, 
without any fire. Though there was, in fact, nothing that could 
justly be considered as surprising in this event, yet I acknowledge 
fairly that it afforded me a degree of childish pleasure, which, 



Facts of Causation and Facts of Sziccession. 59 

were I ambitious of the reputation of a grave philosopher, I ought 
most certainly rather to hide than to discover." ^ 

Here is a phenomenon — the heat of the water in 
Count Rumford's box. Let us inquire now what we 
are doing when we seek for its cause. 

Plainly the motion of the cylinder was an antecedent 
of the heat in the water in some pre-eminent and unique 
sense. Heat is an energy ; it could not appear in the 
wafer unless it passed out of some other material in 
which it previously existed as motion, or in some other 
mode. We know this by a very broad primary induc- 
tion. Indeed, we here come upon the grand generaliza- 
tion of the conservation, or, to use a better word, the 
persistence, of energy. A multitude of experiences 
have led men to believe that whenever energy newly 
appears, it has existed previously in another mode or in 
other materials. The necessary antecedent of energy 
in one mode or one body is the same energy in a pre- 
vious mode or in a different body. All machinery is 
contrived on this principle ; at some point energy is 
introduced, and it is then transferred or transformed, 
so that we get light, heat, electricity or motion, as 
desired. From the standpoint of the physicist the 
whole cause of the heat of the water was the motion 
of the cylinder. The degree of heat gained by the one 
was exactly measured by the amount of motion lost by 
.the other. There was only a transfer of energy. When 
in popular language we say that the motion is the 
cause of the heat, the physicist says that the motion is 
the heat, only in another mode. The law of causation, 
when applied to energy, is only the fact of persistence. 

1 Fktl. Trans. Royal Soc. of London, vol. xviii, pp. 278-282. 



6o Inductive Logic. 

When we say that energy here must have had a cause, 
we only mean that, having no reason to think that new 
energy has been added to the world, we must conse- 
quently assume that this apparently new energy is only 
the old in a new mode. When, therefore, we inquire 
for the cause of energy, we may be merely inquiring, 
Where and in what mode was this energy previously ? 
The answer to the question names the Energetic Cause. 
If it be asked. What was the cause of the motion in 
the cylinder ? the answer is. The motion of the horses. 
The energy might be further traced through physio- 
logical action in the bodies of the horses, and then 
through physiological action in the growth of the grain 
and hay upon which they had fed, until at last we 
should reach the sun's light and heat. One thing is 
now agreed upon, that the stream of energy in the 
world, like the Nile in the desert, receives no tributaries, 
but simply flows on identical with itself, its transforma- 
tions depending upon the qualities and collocations of 
matter. 

But why did motion in the cylinder become heat in 
the water .<* Here a cause is demanded in a different 
sense. The inquiry is for those properties and colloca- 
tions of matter which occasioned a transformation. The 
arrangement was such that motion could not be com- 
municated from the cylinder to any other part of the 
apparatus ; the motion, therefore, according to a per- 
manently coexisting property, transformed itself into 
heat. The different properties of energy and the dif- 
ferent properties of the several sorts of matter in rela- 
tion to energy, we know by primary inductions which 
cannot be resolved into simpler generalizations ; they 



Facts of Causation and Facts of Siiccession. 6 1 

are the ultimate facts of the world. The motion of the 
cylinder changed into heat when the cylinder found 
itself in connection with certain other masses of matter 
of certain qualities and collocations. What were these ? 
The answer to this question will name the Conditional 
Canse. It will describe the environment in which the 
transformation took place. While the motion was the 
cause, and in one sense the sole cause, of the heat, it 
is yet true that, if left to itself, it would never have 
changed to heat ; it would have continued eternally as 
motion. The peculiar environment, then, is, in one 
sense, the sole cause of the heat, since but for that 
there would have been nothing but motion. 

If, instead of investigating the cause of the energy in 
this experiment, we should investigate the cause of the 
matter, asking not. What is the cause of the heat t but, 
What is the cause of the water ? we could go back in 
the same way along an unbroken line of materials. The 
cause of the water in the box was water in a river or a 
well, the cause of that was water in the clouds, the 
cause of that was the two gases oxygen and hydrogen, 
and so on. There is a persistence of matter as there 
is a persistence of force. When we ask for the cause 
of matter in one form or place we may be merely 
inquiring, Where and in what form was this matter 
previously .? The answer will name for us the Material 
Canse. Or we may seek the conditional cause for the 
matter, asking. What was the environment in which this 
matter came to be as it is ">. 

According to one of the grandest primary induc- 
tions of modern science, the two lines of energetic and 
material causation are absolutely continuous and com- 



62 Inductive Logic. 

plete. In the physical world nothing is added and 
nothing is lost ; but the sum of things persists in its 
integrity. 

But approaching the analysis upon a different line, 
we find that Count Rumford himself was in a unique 
sense the cause of the heat. It was his, choice to per- 
form an experiment that eventuated in the heating. 
The Will of Count Rumford was neither the material 
cause, nor the energetic cause, nor the conditional cause 
of the heating of the water. It was the cause in a 
sense higher than any of these. We will call it the 
Volitional Cause. The relation of will to the physical 
universe is peculiar. It cannot originate matter or 
energy; but it can direct the transformation of a 
certain amount of the energy of the body. By taking 
advantage of this power, the Count originated a new 
chain of events, which terminated in the heating. 
When in pursuing a chain of events backward we 
come to a will, the mind recognizes a super-physical 
intervention ; the man is responsible, and if the events 
are injurious to the public welfare, he must pay the 
penalty. All of the power now in my arm was yester- 
day, or previously, in the beef, potatoes, and other food 
on the table. If I allow my arm to hang limp, physi- 
ological and chemical transformations will go forward 
in natural course, and the energy now potentially mine 
will pass away. For a brief space this stored energy 
lies subject to my order, like money in a bank. I can 
will its transformation into motion ; but I cannot 
increase or diminish its amount. A party of Arctic 
explorers, after many days of starvation and hard labor, 
attempted to draw their boat out of the water ; all 



Facts of Causation and Facts of Succession. 63 

grasped it and at the accustomed signal put forth the 
usual volition for simultaneous action. But no effect 
followed ; their wills were as usual, but there was no 
stored energy for those wills to transform. 
Lotze has said : — 

"What constitutes the absolute authority of the causal law is not 
that every part of the finite sum of things actual must in the finite 
sphere be produced by fixed causes, according to universal laws, 
but that each constituent once introduced into this actual course 
continues to act according to these laws. We commonly speak 
only of every effect having its cause, but we should on the con- 
trary lay stress chiefly on the other form of the proposition — 
every cause has invariably its effect. The meaning of causahty 
consists not indeed exclusively, but (it seems to me) in its more 
essential part, in its securing to every element of the actual world, 
springing from no matter what source, means of acting energetic- 
ally on the other constituents of the world to which it belongs, at 
the same time preventing it from acting within that world otherwise 
than in harmony with the universal laws regulating all that takes 
place in it. Thus the world would be like a vortex swelled by 
new waves from all sides, which it does not itself attract or 
produce, but which, once within it, are forced to take part in its 
motion. We have another example of the same process in the 
relation of our own soul to our bodily organs ; the soul evolves 
from itself resolutions, starting-points for future movements ; none 
of them needs to be determined by and founded on phenomena 
in the bodily life on which it reacts ; but each, at the moment of 
its passing into that life, subordinates itself to the peculiar laws of 
the latter, and generates so much or so little motion and force as 
these permit of — motion too in the direction which they prescribe 
and no other. The universal course of things may at every 
moment have innumerable beginnings whose origin lies outside of 
it, but can have none not necessarily continued within it." ^ 

1 Microcosmus, p. 260. I am indebted for this quotation to my col- 
league, Professor Henry C. King. 



64 Inductive Logic. 

Lotze is wrong in saying that the will generates 
force and thus adds to the sum of physical things ; but 
he is right in saying that the spiritual acts upon the 
physical to transform energy, and that, once transformed, 
the energy goes on acting according to the uniformity 
of its coexistences, or what are commonly called its 
laws. The beginnings which lie outside of the uni- 
versal course of physical things are volitions, and their 
effects are transformations. The will is not the ener- 
getic cause any more than it is the material cause ; it 
is a cause stu generis, the volitional cause. 

So far we have spoken of Things as the causes of 
Things. Matter in one form or situation is the cause 
of the same matter differently disposed ; energy as 
motion is the cause of the same energy as heat ; a 
Will, by transforming the vital energy of the body into 
various motions, brings together matter and energy in 
new combinations. The causes so far considered are 
entities and the effects are entities. 

But things may also cause Events. Every kind of 
matter and every kind of energy has uniform properties ; 
it reacts in certain ways upon other things. These 
reactions are called its effects. In this aspect each 
thing may be called an Efficient Cause. In our exper- 
iment there were certain events, the moving of the 
cylinder, the heating of the water, etc. The energy 
concerned was the efficient cause of these events. 
Count Rumford was also an efficient cause of the 
events, since the action of his will was concerned in 
their production. 

But an entirely different line of investigation might 
have been pursued ; leaving things entirely out of view, 



Facts of Causation and Facts of Succession. 65 

we might have attended solely to Events. One event 
may be said to cause another event. 

The ultimate qualities of matter and force remaining 
as they are, in every possible collocation of things 
(except that of perfect equilibrium), a certain reaction 
is inevitable. If, for example, it be the nature of water 
to absorb heat, then when a quantity of water, as in 
Count Rumford's box, finds itself in contact with a hot 
cylinder, the absorption will inevitably take place. But 
every physical event is simply a new distribution of 
forces and materials : hence (the properties of things 
remaining as they are) a further reaction is inevitable. 
Thus, like the bits of colored glass in a kaleidoscope, 
the things in the physical world fall at each moment 
into new relations each of which, if there be no inter- 
vention, is the necessary opportunity for the next. 
Thus one event is said to cause another event. This 
inevitableness of physical reaction is the very fact 
which opens the door for the interventions of will. 
By transforming the energy of the body into motion, 
and thus changing the collocations of a few things, 
men shunt on to other tracks the trains of events and 
transform the whole complexion of history. 

Recurring to the experiment, we may say that the 
moving of the cyhnder was an event which caused the 
heating of the water, another event. But when rigid 
definition is attempted it is found surprisingly difficult 
to define an event. The event was not merely the 
heating of some water, but the heating of it in a cer- 
tain box at a particular time and place and in peculiar 
circumstances. When all the circumstances, even the 
most remote, are taken into the account, they include 



66 Inductive Logic. 

the situation of the whole universe. The successive 
events of history are the successive collocations of the 
totality of things. While this is true, the general facts 
of the universe are so permanent and so similar as 
factors in all events that they may be practically dis- 
regarded, and the more detailed and proximate elements 
alone considered as constituting an event. The name 
Historical Cause may be given to one event when 
regarded as the cause of another event. Notice how 
different is the sense of the word cause here from that 
which it bears when applied to things. An event is 
the cause of another event only in the sense that its 
occurrence is the coming of materials and forces into 
such a collocation that they are certain to react again 
in a particular way. The turning of the cylinder was 
an event ; but if a cylinder be turning under such 
circumstances, it is the ultimate property of motion to 
become heat and of water to absorb heat; consequently 
the turning was the historical cause of the heating. 
Between events there can be no connection but that of 
succession ; they are but the coming of things into 
collocations. The continuity is in the things, and each 
new event arises out of the ultimate properties which 
coexist in things. There is no efficiency in an event, 
or tendency of any kind to beget another event; but 
after each event there is a new possibility; and, the 
properties of matter and force remaining persistent, 
whatever is possible is inevitable. When a siphon has 
been filled with water and is left open, the force of 
gravity will cause the water to flow until the short end 
of the tube is exposed. The filling and opening of the 
siphon are events which leave a situation in which 



Facts of Causation and Facts of Succession. 6/ 

gravity can cause a flow, but those events have no 
efficiency in inducing the flow. Popularly, the fall- 
ing of a spark into a powder magazine is said to cause 
an explosion. Historically this is correct ; when a 
spark so falls there is a collocation in which heat will 
pass into materials which at that temperature will enter 
into new chemical combinations accompanied by that 
sudden distension which is called an explosion. The 
falling of the spark is the historical cause, the spark 
and the powder are the material cause, the heat of the 
spark and the chemical affinity of the substances con- 
stituting the powder are the energetic cause. 

In a loose way, an event may be said to be the cause 
of a State. A blackened pile of ruins may be pointed 
out as the effects of a conflagration, or the splintered 
trunk of a tree may be called the effect of lightning. 
But, strictly speaking, states have no causes. No 
reason need be given why things remain as they are ; 
for obviously, unless something happens, nothing hap- 
pens. If a ball is in motion, and no obstruction 
presents itself, we do not have to account for the 
motion ; but if the ball stops, there is an event to 
account for. An event is the coming of things into a 
new situation. If in this situation there is a com- 
parative equilibrium of forces, the situation may 
indefinitely continue. If the breaking of a dam allows 
the water to flow out, the event of the breaking is the 
historical cause of the event of the emptying. But the 
reservoir may never be filled again ; the state of empti- 
ness may continue permanently, and the cause for it 
will be said to be the breaking of the dam. This, 
however, is a very inexact use of language. Emptiness 



6S Inductive Logic. 

is a mere negation. The thing to be accounted for is 
the change from the previous fullness. The breach in 
the dam leaves the water free to move, under the 
efficient cause, gravity ; once empty, the reservoir 
remains so without needing a cause of any kind. 

Human history moves on in the midst of a complex 
of materials and forces which have certain properties, 
and which are certain, in each given collocation, to react 
in one particular way. Physically speaking, whatever 
at any moment is possible is certain. There is no 
contingency, no alternative. A weight free to fall 
falls; a bit of iron in a jar of oxygen and sufficiently 
hot burns. Each event makes possible the next, and 
in that sense may be said to make it certain. But the 
human will has the wonderful power of choosing which 
of several events shall come to pass. It cannot create 
nor annihilate matter or energy ; but it can transform 
the energy of the body into motion. Thus materials 
and forces may be brought into collocations which 
would not otherwise have arisen and, although reacting 
according to their nature, may produce events very 
different from what would otherwise have been. The 
volitions of will do not arise by necessity out of fore- 
going situations; consciousness affirms freedom, and it 
is here our only organ of observation. The motives 
in view of which will acts are Occasional Causes, not 
efficient causes. In tracing the course of events in 
human history we find this interweaving of physical 
necessities and free volitions like the warp and woof of 
a tapestry : to unravel it, is the task of the historian in 
his search for the connections of things. A passage 
from the Life and Letters of Charles Darwin will show 



Facts of Causation and Facts of Succession. 69 

how slight may be the connection between two events 
which are yet in a certain sense cause and effect : — 

"The following story shows what good guesses my father 
could make. Lord Shelburne, afterward the first Marquis of 
Lansdowne, was famous (as Macaulay somewliere remarks) for his 
knowledge of the affairs of Europe, on which he greatly prided 
himself. He consulted my father medically, and afterward 
harangued him on the state of Holland. My father had studied 
medicine at Leyden, and one day while there went on a long walk 
into the country with a friend who took him to the house of a 

clergyman (we will say the Rev. Mr. A , for I have forgotten 

his name), who had married an Englishwoman. My father was 
very hungry, and there was little for luncheon except cheese, 
which he could never eat. The old lady was surprised and 
grieved at this, and assured my father that it was an excellent 
cheese, and had been sent to her from Bowood, the seat of Lord 
Shelburne. My father wondered why a cheese should be sent to 
her from Bowood, but thought nothing more about it until it 
flashed across his mind many years afterwards, whilst Lord 
Shelburne was talking about Holland. So he answered, 'I should 

think from what I saw of the Rev. Mr. A , that he was a very 

able man, and well acquainted with the state of Holland.' My 
father saw that the Earl, who unmediately changed the conver- 
sation, was much startled. On the next morning my father 
received a note from the Earl, saying that he had delayed starting 
on his journey, and wished particularly to see my father. When 
he called, the Earl said, 'Dr. Darwin, it is of the utmost impor- 
tance to me and to the Rev. Mr. A to learn how you have 

discovered that he is the source of my information about Holland.' 
So my father had to explain the state of the case, and he supposed 
that Lord Shelburne was much struck with his diplomatic skill in 
guessing, for during many years afterwards he received many kind 
messages from him through various friends. I think that he 
must have told the story to his children ; for Sir C. Lyell asked 
me many years ago why the Marquis of Lansdowne (the son or 
grandson of the first marquis) felt so much interest about me, 
whom he had never seen, and my family. When forty new mem- 



70 Inductive Logic. 

bers (the forty thieves, as they were then called) were added to 
the Athenaeum Club, there was much canvassing to be one of 
them ; and without my having asked any one. Lord Lansdowne 
proposed me and got me elected. If I am right in my supposi- 
tion, it was a queer concatenation of events that my father not 
eating cheese half-a-century before in Holland led to my election 
as a member of the Athenaeum." ^ 

This " queer concatenation " is a fair example of 
causation in human history. Dr. Darwin's not eating 
cheese was the cause of his son's being elected into 
the club, that is, it was a link in a chain of events, 
some of which were volitions and some physical neces- 
sities, and the election was a subsequent link. The 
very triviality of this incident makes it especially good 
as an illustration. We have termed the motives upon 
which the will reacts, occasional causes, since they 
furnish the occasions, but not the efificiency, of causa- 
tion. Here maybe distinguished the Formal Cause, or 
idea viewed as a distinct conception ; and Final Cause, 
the end, design, or object for which anything is done. 

A Negative Cause is the absence of anything which if 
present would have prevented a given phenomenon. It 
is obvious that any particular event would not have 
happened if it had been prevented. The absence of a 
violent earthquake was a negative cause of the heating 
of the water in Count Rumford's experiment. But the 
word cause is used here in a sense very remote from 
that which it bears in other connections. A little boy 
said that salt was the cause of a bad taste in potatoes 
when he did not put it on them. That is, in the 
absence of salt, potatoes have an insipid taste. To say 
"negative cause" is, indeed, to make a contradiction 

1 Page 14. 



Facts of Causation and Facts of Succession. 71 

in the adjective ; it is equivalent to "inactive agent." 
But in common life, and in ordinary discourse, it is 
convenient, when the absence of some usual factor in 
a collocation of things gives opportunity for some 
unusual event. Thus the absence of the signalman is 
said to be the negative cause of the railway accident, 
and the sleep of the sentinel is said to be the negative 
cause of the defeat of the army. A will may be a 
negative cause in a more active sense, since refusal to 
interfere, when interference is possible, involves at least 
consent to the occurrence of the event; hence, neglect 
may be criminal. 

Let us sum up now the results of our discussion of 
Causation. The cause of a phenomenon is that which 
gives it existence. Every mass of matter has a mate- 
rial cause, which is the same matter in a previous place 
or state. Every portion of energy has an energetic 
cause, which is the same energy in a previous mode or 
another mass of matter. Every portion of matter or 
of energy has a conditional cause for its present place 
and form, in the environment which has reacted upon it. 
One peculiar factor in the conditional cause may be a 
will whose reaction transforms energy, thus constitut- 
ing a volitional cause. A will acts in view of motives, 
occasional causes. Events are the reactions of things, 
which are their efficient causes. 

Is the law of causation, namely, that every phenome- 
non depends upon some other phenomenon, intuitively 
known } The question is too vague to admit of a 
single answer. That matter and energy persist is a 
very recently made primary induction from experience. 
The law of material and of energetic causation is, then. 



72 Inductive Logic. 

not intuitively known. That every event has a thing 
as its cause is known by a mere analysis of the mean- 
ing of the terms employed, since events are the reactions 
of things, and there cannot be an action without an 
agent. That every event has some other event as its 
necessary historical cause is not proved either from 
intuition or experience. Gravitation causes the earth 
to revolve around the sun ; the causation is in the 
bodies and forces, not in any previous event. That a 
will acts in view of final and formal causes is plain ; 
but that, like matter, it always reacts in precisely the 
same way under the same stimulus is contradicted by 
consciousness. 

Do we know intuitively that "like causes always 
produce like effects " t The difficulty with this ques- 
tion is that the words cause and effect are correlatives, 
and must be defined in terms of each other. An 
affirmative answer would teach nothing but an identical 
proposition. The truth which the dictum seeks to 
express is better stated thus : We know by a primary 
induction that the existing order persists, and while 
things remain as they are they will act as they do. 
How long the existing order will continue we cannot 
even guess, since all of our reasoning about things is 
based upon primary inductions from the existing order. 
But neither have we any ground for expecting an end. 

The foregoing discussion of facts of causation makes 
it easy to deal with facts of succession. The facts of 
succession are seen to be all secondary. They are 
incidental results of facts of causation. Succession is 
not at all of the essence of causation. Gravitation 
keeps the earth revolving around the sun. This effect 



Facts of CaiLsation and Facts of Succession. 73 

is the operation of a permanent cause — the two bodies 
reacting upon each other ; but there is no succession 
of cause and effect. Just so the needle is attracted 
toward the pole by a permanent cause, magnetism. 
Succession belongs to events in their mutual relations, 
not to things ; but things are the only efficient causes. 
Things coexist and persist ; they do not follow one 
another in time. It is true that between a thing and 
the material cause of it, that is, the same matter in an 
earlier form, there is a sort of succession. Ice may 
cause water, and water may cause steam ; one form 
follows another. But this is not at all that invariable 
sequence which constitutes a fact of succession. Things 
must be simultaneous with their own reactions. Pro- 
fessor Davis remarks: — 

" But it would, perhaps, be more accurate to say that every cause 
is simultaneous with its effect. For cause and effect are correla- 
tives — neither can exist without the other; they exist only as 
they coexist. A cause cannot be so named, except by anticipation, 
until there is an effect ; nor an effect, except by reference to what 
has already occurred, after the change or event has taken place. 
The order of succession is logical, not temporal." ^ 

The fact that events occupy time, and the fact that 
each event leaves a new collocation of things which 
makes a new reaction possible — these two facts give 
us the chain of history. Between two events, one of 
which is the historical cause and the other the his- 
torical effect, there is no other connection than that, 
after the first, things are in such a collocation that they 
cause the second. An event has as many possible 
historical causes as there are possible ways of bringing 

1 Inductive Logic, p- 23. 



74 Inductive Logic, 

things into the requisite collocation. For example, ice 
when in contact with salt at ordinary temperatures of 
the air rapidly liquefies. The efficient cause of the 
event, liquefaction, is the two bodies ice and salt, and 
they are simultaneous with it. But the historical cause 
of the event is any possible action which can bring the 
substances together, and thus open the possibility for 
their reaction. All facts of succession are thus conse- 
quences of facts of coexistence and causation. A 
succession is known empirically, and is susceptible of 
analysis into simpler elements. We may always hope 
to be able to tell why a given succession obtains, in 
terms of facts of coexistence and causation. Yet many 
successions were empirically known ages before they 
were analyzed, and many well-known successions still 
remain unanalyzed. Many persons are familiar with 
that historical succession of events which always ends 
in the production of ice-cream, who have never thought 
of the operation of the efficient causes. 



CHAPTER X. 
MR. MILL'S DOCTRINE OF CAUSATION. 

Mr. John Stuart Mill is unquestionably the most 
eminent and influential of all writers upon inductive 
logic since Bacon. His work is the most elaborate 
that has appeared, and his teachings, on many points, 
have been generally adopted. The science owes to him 
a very great debt. No one can justly claim to under- 
stand modern inductive logic who has not thoroughly 
studied Mr. Mill's doctrine of causation. In this 
chapter we shall seek to present this doctrine in a 
condensed form, but as nearly as possible in Mr. Mill's 
own words. 

According to Mr. Mill, the notion of cause is "the 
root of the whole theory of Induction." In this view 
he is followed by later writers. For example. Professor 
Davis says : " Such principles are evolved from the 
intuitive fact of causation, the root of all induction, 
and that which gives it validity." 

Yet Mr. Mill also holds that our first step in the 
knowledge of nature is to discover the particular 
uniformities; then that we generalize the uniformity 
of these uniformities ; and that this uniformity of 
uniformities is the law of the uniformity of nature. 
Strangely enough, the uniformity of nature is, to Mr. 
Mill, the same as the law of causation. " Whatever be 
the most proper mode of expressing it," he says, "the 
proposition that the course of nature is uniform, is the 
fundamental principle, or general axiom of induction." 



"J 6 Inductive Logic. 

It is a difficulty with this view that if inductive logic 
have to do solely with causation, the vast mass of facts 
of coexistence and of resemblance is left unprovided 
for. Such sciences as mineralogy and botany deal 
mainly with facts of coexistence, yet they are com- 
monly considered purely inductive. The definition 
provides no rightful place in inductive logic for the 
original discovery of uniformities; all of this work has 
been done before induction proper can begin. More- 
over, the law of uniformity of uniformities is something 
very much wider than the law of causation. It is 
largely concerned with the uniformities of coexistence. 
Thus we know the persistence of the several kinds of 
matter and the persistence of energy by so many inde- 
pendent primary inductions from multitudinous obser- 
vations of the several things. We not only know that 
a magnet attracts iron, which is a fact of causation; 
but that iron remains iron, that is, that that assemblage 
of coexisting qualities which we call iron persists, 
which is not a fact of causation. 

Mr. Mill does not regard the uniformity of nature as 
"the immediate major premise in every inductive argu- 
ment." " It is not a necessary condition that the 
uniformity should pervade all nature. It is enough 
that it pervades the particular class of phenomena to 
which the induction relates." That is, we may make a 
valid secondary induction from any sound, though 
limited, primary induction, without reference to the 
soundness of the root of the whole theory. In fact the 
so-called root is only a generalization of more limited 
primary inductions. 

Mr. Mill's definition of Cause is as follows : — 



Mr. Mill's Doctrine of Causation. J'J 

" We may define, therefore, the cause of a phenomenon, to be 
the antecedent, or the concurrence of antecedents, on which it is 
invariably and unconditionally consequent." 

In making this definition Mr. Mill began with no 
analysis of the different ways in which the word cause 
is used. He did not inquire whether the so-called 
effect is a thing or a reaction, or the so-called cause a 
material, an energy, a circumstance, a will, or a prior 
event. Starting with the notion of succession as 
fundamental, he attempted to frame a definition so 
general as to cover all values of the unknown terms of 
the relation. Yet it is plain in the course of his 
elaborate discussions that, generally, for him the 
"phenomenon" in the definition is a reaction, an 
event. For he says : — 

"And the universality of the law of causation consists in this, 
that every consequent is connected in this manner with some par- 
ticular antecedent, or set of antecedents. Let the fact be what it 
may, if it has begun to exist, it was preceded by some fact or 
facts, with which it is invariably connected. For every event 
there exists some combination of objects or events, some given 
concurrence of circumstances, positive and negative, the occur- 
rence of which is always followed by that phenomenon." "On 
the universality of this truth depends the possibility of reducing 
the inductive process to rules." ^ 

For Mr. Mill, then, an effect is an event, and a cause 
is a number of things in a collocation and with a 
history. 

In this complex of things, relations, and history, to 
which alone Mr. Mill, when speaking strictly, gives the 
name cause, all the factors are absolutely equal. The 

1 Logic, p. 237. 



y8 Inductive Logic. 

difference between efficient causes and conditions is 
denied. Mr. Mill says : — 

"It is seldom, if ever, between a consequent and one single 
antecedent, that this invariable sequence subsists. It is usually 
between a consequent and the sum of several antecedents; the 
concurrence of them all being requisite to produce, that is, to be 
certain of being followed by, the consequent. In such cases it is 
very common to single out one only of the antecedents under the 
denomination of Cause, caUing the others merely Conditions. 
Thus, if a man eats of a particular dish, and dies in consequence, 
that is, would not have died if he had not eaten of it, people would 
be apt to say that eating of that dish was the cause of his death. 
There need not, however, be any invariable connection between 
eating of the dish and death; but there certainly is, among the 
circumstances which took place, some combination or other upon 
which death is invariably consequent : as, for instance, the act of 
eating of the dish, combined with a particular bodily constitution, 
a particular state of present health, and perhaps even a certain 
state of the atmosphere; the whole of which circumstances, per- 
haps, constituted in this particular case the conditions of the 
phenomenon, or in other words, the set of antecedents which 
determined it, and but for which it would not have happened. 
The real Cause, is the whole of these antecedents; and we have, 
philosophically speaking, no right to give the name of cause to 
one of them, exclusively of the others. What, in the case we have 
supposed, disguises the incorrectness of the expression, is this: 
that the various conditions, except the single one of eating the 
food, were not events (that is, instantaneous changes, or succes- 
sions of instantaneous changes) but states, possessing more or less 
of permanency; and might, therefore, have preceded the effect by 
an indefinite length of duration, for want of the event which was 
requisite to complete the required concurrence of conditions: while 
as soon as that event, eating the food, occurs, no other cause is 
waited for, but the effect begins immediately to take place: and 
hence the appearance is presented of a more immediate and closer 
connection between the effect and that one antecedent, than 
between the effect and the remaining conditions. But though we 



Mr. Mill's Doctrine of Causation. 79 

may think proper to give the name of cause to that one condition 
the fulfillment of which completes the tale and brings about the 
effect without further delay, this condition has really no closer 
relation to the effect than any of the other conditions has. All the 
conditions were equally indispensable to the production of the 
consequent; and the statement of the cause is incomplete, unless, 
in some shape or other, we introduce them all. A man takes 
mercury, goes out of doors, and catches cold. We say, perhaps, 
that the cause of his taking cold was exposure to the air. It is 
clear, however, that his having taken mercury may have been a 
necessary condition of his catching cold; and though it might 
consist with usage to say that the cause of his attack was exposure 
to the air, to be accurate we ought to say that the cause was 
exposure to the air while under the effect of mercury. 

"If we do not, when aiming at accuracy, enumerate all the 
conditions, it is only because some of them will, in most cases, be 
understood without being expressed, or because for the purpose in 
view they may, without detriment, be overlooked. For example, 
when we say, the cause of a man's death was that his foot slipped 
in climbing a ladder, we omit, as a thing unnecessary to be stated, 
the circumstance of his weight, though quite as indispensable a 
condition of the effect which took place." 

" In all these instances the fact which was dignified by the 
name of cause, was the one condition which came last into exist- 
ence. But it must not be supposed that in the employment of the 
term, this or any other rule is always adhered to. Nothing can 
better show the absence of any scientific ground for the distinc- 
tion between the cause of a phenomenon and its conditions, than 
the capricious manner in which we select from among the condi- 
tions that which we choose to denominate the cause. However 
numerous the conditions may be, there is hardly any of them 
which may not, according to the purpose of our immediate 
discourse, obtain that nominal pre-eminence." ^ 

" Thus we see that each and every condition of the phenomenon 
may be taken in its turn, and with equal propriety in common 
parlance, but with equal impropriety in scientific discourse, may be 

1 Logic, pp. 237, 238. 



8o Inductive Logic. 

spoken of as if it were the entire cause. And in practice that 
particular condition is usually styled the cause whose share in the 
matter is superficially the most conspicuous, or whose requisite- 
ness to the production of the effect we happen to be insisting 
upon at the moment. So great is the force of this last considera- 
tion, that it often induces us to give the name of cause even to 
one of the negative conditions. We say, for example, the cause 
of the army's being surprised was the sentinel's being off his post. 
But since the sentinel's absence was not what created the enemy, 
or made the soldiers to be asleep, how did it cause them to be 
surprised ? All that is really meant is, that the event would not 
have happened if he had been at his duty. His being off his post 
was no producing cause, but the mere absence of a preventing 
cause : it was simply equivalent to his non-existence. From 
nothing, from a mere negation, no consequences can proceed. 
All effects are connected, by the law of causation, with some set 
of positive conditions; negative ones, it is true, being almost 
always required in addition. In other \vords, every fact or 
phenomenon which has a beginning, invariably arises when some 
certain combination of positive facts exists, provided certain other 
positive facts do not exist." ^ 

" The cause, then, philosophically speaking, is the sum total of 
the conditions, positive and negative, taken together; the whole of 
the contingencies of every description, which being realized, the 
consequent invariably follows." ^ 

In this great definition Mr. Mill provides for no 
effects but events, and for no causes but complexes of 
things, of collocations, and of history. 

" The state of the whole universe at any instant, we believe to 
be the consequence of its state at the previous instant : insomuch 
that one who knew all the agents which exist at the present 
moment, their collocation in space, and all their properties, in other 
words, the laws of their agency, could predict the whole subsequent 
history of the universe, at least unless some new volition of a 
power capable of controlling the universe should supervene." ^ 

1 Logic, p. 239. 2 ibid.^ p. 241. 3 jbid.^ p. 250. 



Mr. Mill's Doctrme of Causation. 8i 

The cause of the heating of the water in Count 
Rumford's box, then, and the only thing to which 
a philosopher can give the name of cause, was the 
immediately previous state of the universe. And 
what we have learned from the experiment is the in- 
variable and unconditional succession between that 
state of the universe and the heating of just such a box 
of water. But since the universe never was before in 
just that state, and never will be again, it is hard to see 
that we have learned anything at all. Mr. Mill refuses 
to recognize any difference in the relations of the dif- 
ferent sorts of causes to the event. "All the positive 
conditions of a phenomenon are alike agents, alike 
active." ^ 

Although it was with the notion of succession that 
Mr. Mill began his definition of cause, yet he did not 
hold to it with great firmness. He inquires : — 

" Does a cause always stand with its effect in the relation of 
antecedent and consequent? Do we not often say of two simul- 
taneous facts that they are cause and effect — as when we say 
that fire is the cause of warmth, the sun and moisture the cause of 
vegetation, and the like? Since a cause does not necessarily 
perish because its effect has been produced, the two, therefore, do 
very generally coexist ; and there are some appearances, and some 
common expressions, seeming to imply not only that causes may, 
but that they must, be contemporaneous with their effects. 
Cessante causa, cessat et effectiis, has been a dogma of the 
schools : the necessity for the continued existence of the cause in 
order to the continuance of the effect, seems to have been once 
a general doctrine among philosophers. Kepler's numerous 
attempts to account for the motion of the heavenly bodies on 
mechanical principles, were rendered abortive by his always sup- 

1 Logic, p. 243. 



82 Inductive Logic. 

posing that the force which set those bodies in motion must 
continue to operate in order to keep up the motion which it at 
first produced. Yet there were at all times many familiar in- 
stances in open contradiction to this supposed axiom. A coup de 
soleil gives a man a brain fever : will the fever go off as soon as 
he is moved out of the sunshine ? A sword is run through his 
body : must the sword remain in his body in order that he may 
continue dead 1 A ploughshare once made, remains a plough- 
share, without any continuance of heating and hammering, and 
even after the man who heated and hammered it has been gath- 
ered to his fathers. On the other hand, the pressure which 
forces up the mercury in an exhausted tube must be continued in 
order to sustain it in the tube. This (it may be replied) is 
because another force is acting without intermission, the force 
of gravity, which would restore it to its level, unless counterpoised 
by a force equally constant. But again : a tight bandage causes 
pain, which pain will sometimes go off as soon as the bandage is 
removed. The illumination which the sun diffuses over the earth 
ceases when the sun goes down. 

" There is therefore a distinction to be drawn. The conditions 
which are necessary for the first production of a phenomenon, are 
occasionally also necessary for its continuance; but more com- 
monly its continuance requires no conditions except negative 
ones. Most things, once produced, continue as they are, until 
something changes or destroys them; but some require the perma- 
nent presence of the agencies which produced them at first. These 
may, if we please, be considered as instantaneous phenomena, 
requiring to be renewed at each instant by the cause by which 
they were at first generated. Accordingly, the illumination of any 
given point of space has always been looked upon as an in- 
stantaneous fact, which perishes and is perpetually renewed as 
long as the necessary conditions subsist. If we adopt this lan- 
guage, we are enabled to avoid admitting that the continuance of 
the cause is ever required to maintain the effect. We may say, it 
is not required to maintain, but to reproduce the effect, oi else to 
counteract some force tending to destroy it. And this may be a 
convenient phraseology. But it is only a phraseology. The fact 
remains that in some cases (though these are a minority) the con- 



Mr. Mill's Doctrine of Causation. 83 

tinuance of the conditions which produced an effect is necessary 
to the continuance of the effect. 

" As to the ulterior question, whether it is strictly necessary 
that the cause, or assemblage of conditions, should precede, by 
ever so short an instant, the production of the effect (a question 
raised and argued with much ingenuity by a writer from whom 
we have quoted), we think the inquiry an unimportant one. 
There certainly are cases in which the effect follows without an 
interval perceptible to our faculties ; and when there is an interval, 
we cannot tell by how many intermediate lines imperceptible to 
us that interval may really be filled up. But even granting that 
an effect may commence simultaneously with its cause, the view 
I have taken of causation is in no way practically affected. 
Whether the cause and its effect be necessarily successive or not, 
causation is still the law of the succession of phenomena. Every- 
thing which begins to exist must have a cause; what does not 
begin to exist does not need a cause; what causation has to 
account for is the origin of phenomena, and all the successions of 
phenomena must be resolvable into causation. These are the 
axioms of our doctrine. If these be granted, we can afford, 
though I see no necessity for doing so, to drop the words ante- 
cedent and consequent as applied to cause and effect. I have no 
objection to define a cause, the assemblage of phenomena, which 
occurring, some other phenomenon invariably commences, or has 
its origin. Whether the effect coincides in point of time with, or 
immediately follows, the hindmost of its conditions, is immaterial. 
At all events it does not precede it ; and when we are in doubt, 
between two coexistent phenomena which is cause and which 
effect, we rightly deem the question solved if we can ascertain 
which of them preceded the other." ^ 

This admission cannot but be regarded as most 
damaging for the definition. Mr. Mill's confusion here 
arises from not having discriminated the various senses 
of the words cause and effect, and from not having dis- 
tinguished between matter, energy, persons, events, 

1 Logic, pp. 247, 248. 



84 Inductive Logic. 

states, and historical concatenations which are mere 
sequences of possibilities. The effects which Mr. Mill 
finds following their causes are states; the effects 
which are simultaneous with their causes are events. 
When a ball is struck, the motion of the bat passes into 
it; that effect is simultaneous. But the state of motion 
once begun continues indefinitely ; this effect there- 
fore follows its cause, the blow. Strictly speaking, the 
cause of an event cannot precede that event. Count 
Rumf ord existed, it is true, before his experiment ; and 
in that sense the cause preceded the effect. But, when 
living under the name of Benjamin Thompson in Con- 
necticut, he was in no proper sense the cause of the 
experiment years later in Munich. He might have 
been slain in the war of the Revolution and never 
have gone to Munich at all. He was not really the 
cause of the experiment until he performed it. Things 
exist permanently, and of course both precede and 
follow their effects. Particular events are always 
simultaneous with their causes, the things that react. 
States continue indefinitely after the events that intro- 
duce them. Events in history precede the events for 
which they open the way, and of which they are there- 
fore called the causes. 

Mr. Mill says: "The law of Causation, the recogni- 
tion of which is the main pillar of inductive science, is 
but the familiar truth that invariability of succession is 
found by observation to obtain between every fact in 
nature and some other fact which has preceded it." 
But this language is exceedingly liable to mislead a 
hasty reader into thinking that Mr. Mill means to say 
that each particular fact has some other particular fact 



Mr. Mill's Doctrine of Causation. 85 

as its cause. " It is seldom, if ever, between a con- 
sequent and a single antecedent, that this invariable 
sequence subsists." In truth, the facts between which 
Mr. Mill asserts invariability of succession are states 
of the universe. "The cause," he says, "is the sum 
total of the conditions, positive and negative, taken 
together ; the whole of the contingencies of every 
description." "The state of the whole universe at 
any instant, we believe to be the consequence of its 
state at the previous instant." 

Mr. Mill understands his definition to mean that the 
cause is the sum total of the conditions "immediately, 
not remotely, preceding the effect." But it is hard to 
reconcile this interpretation with the explanations which 
place historical events among the antecedents. If 
taking mercury and subsequently being exposed to the 
air are among the conditions of a man's death, the 
cause cannot be the total of the immediately antecedent 
conditions. Mr. Mill escapes the difficulty by saying, 
that remote events are conditions of the conditions ; 
they are not the causes, but the causes of the causes ; 
or rather factors of the causes of factors of the cause. 

Mr. Mill felt that there must be something in causa- 
tion more than mere invariable succession. There 
must be something which other writers had attempted 
to express by the term necessity, and for this he 
'selected the word unconditionalness . He says : — 

"Jf there be anything which confessedly belongs to the term 
necessity, it is uncojiditionalness. That which is necessary, that 
which 7nust be, means that which will be, whatever supposition we 
may make in regard to other things. The succession of day and 
night evidently is not necessary in this sense. It is conditional 



S6 Inductive Logic. 

on the occurrence of other antecedents. That which will be fol- 
lowed by a given consequent when, and only when, some third 
circumstance also exists, is not the cause, even though no case 
should ever have occurred in which the phenomenon took place 
without it." 1 

Returning to the definition, we find the cause to be 
the antecedent or concurrence of antecedents, that is, a 
complex ; but a complex of what } Of conditions, all 
equally essential. It is the assemblage that constitutes 
the particular cause. When we are told that the con- 
sequent must be unconditionally consequent upon the 
assemblage of these conditions, what is that but to 
learn that the assemblage of conditions must lack no 
condition, that is, must be complete t What Mr. Mill 
wanted to say was that no superfluous circumstance, 
nothing that does not have some efficiency, must be 
counted among the conditions. But since, according to 
his doctrine, the cause, philosophically viewed, is the 
immediately previous state of the universe, and since 
inductive science knows nothing about efficiency, this 
is difficult to avoid. 

Let us revert, parenthetically, to the question whether 
day is the cause of night, and night the cause of day. 
This question illustrates the necessity of an analysis of 
terms before beginning to discuss about facts. All 
light is not day, nor is all darkness night. The 
darkness in the Mammoth Cave is not night, nor is 
the illumination of the cave, by the combustion of 
magnesium, day. A day is that portion of the sun's 
illumination which is cut off and individualized by two 
nights. As soon as this is stated, it is seen that night 

1 Logic, p. 245. 



Mr. Mill's Doctrine of Causation. Sy 

is the cause of day. At the north pole there is but 
one day in the year, because there is but one night. 
But in what sense is night the cause of day ? It is not 
the efficient cause, nor the material cause, nor the 
conditional cause, but simply the historical cause. The 
event, an interruption of light by rotation, makes a 
possibility for a restoration of light by rotation. If one 
event did not occur, the other could not occur ; the 
occurrence of night is an essential condition of the 
occurrence of day. 

Mr. Mill holds that the actions of the Will are under 
exactly the same laws of causation as the reactions of 
matter. He says : — 

" The question, whether the law of causality applies in the same 
strict sense to human actions as to other phenomena, is the cel- 
ebrated controversy concerning the freedom of the will ; which, 
from at least as far back as the time of Pelagius, has divided both 
the philosophical and the religious world. The affirmative opinion 
is commonly called the doctrine of Necessity, as asserting human 
volitions and actions to be necessary and inevitable. The negative 
maintains that the will is not determined, like other phenomena, 
by antecedents, but determines itself ; that our volitions are not, 
properly speaking, the effects of causes, or at least have no causes 
which they uniformly and implicitly obey. 

" I have already made it sufficiently apparent that the former of 
these opinions is that which I consider the true one ; but the mis- 
leading terms in which it is often expressed, and the indistinct 
manner in which it is usually apprehended, have both obstructed 
its reception, and perverted its influence when received. The 
metaphysical theory of free will, as held by philosophers (for the 
practical feeling of it, common in a greater or less degree to all 
mankind, is in no way inconsistent with the contrary theory), was 
invented because the supposed alternative of admitting human 
actions to be necessary, was deemed inconsistent with every one's 
instinctive consciousness, as well as humiliating to the pride and 



88 Inductive Logic. 

even degrading to the moral nature of man. Nor do I deny that 
the doctrine, as sometimes held, is open to these imputations ; for 
the misapprehension in which I shall be able to show that they 
originate, unfortunately is not confined to the opponents of the 
doctrine, but participated in by many, perhaps we might say by 
most of its supporters. 

" Correctly conceived, the doctrine called Philosophical Neces- 
sity is simply this : that, given the motives which are present to 
an individual's mind, and given likewise the character and disposi- 
tion of the individual, the manner in which he will act may be 
unerringly inferred ; that if we knew the person thoroughly, and 
knew all the inducements which are acting upon him, we could 
foretell his conduct with as much certainty as we can predict any 
physical event. This proposition I take to be a mere interpretation 
of universal experience, a statement in words of what every one 
is internally convinced of. No one who believed that he knew 
thoroughly the circumstances of any case, and the characters of 
the different persons concerned, would hesitate to foretell how all 
of them would act. Whatever degree of doubt he may in fact 
feel, arises from the uncertainty whether he really knows the 
circumstances, or the character of some one or other of the 
persons, with the degree of accuracy required ; but by no means 
from thinking that if he did know these things, there could be any 
uncertainty what the conduct would be. Nor does this full 
assurance conflict in the smallest degree with what is called our 
feeling of freedom. We do not feel ourselves the less free, 
because those to whom we are intimately known are well assured 
how we shall will to act in a particular case. We often, on the 
contrary, regard the doubt what our conduct will be, as a mark of 
ignorance of our character, and sometimes even resent it as an 
imputation. It has never been admitted by the religious philos- 
ophers who advocated the free-will doctrine, that we must feel not 
free because God foreknows our actions. We may be free, and 
yet another may have reason to be perfectly certain what use we 
shall make of our freedom. It is not, therefore, the doctrine that 
our volitions and actions are invariable consequents of our ante- 
cedent states of mind, that is either contradicted by our conscious- 
ness, or felt to be degrading. 



Mr. Mill's Doctrine of Causation. 89 

"But the doctrine of causation, when considered as obtaining 
between our voHtions and their antecedents, is almost universally- 
conceived as involving more than this. Many do not believe, and 
very few practically feel, that there is nothing in causation but 
invariable, certain, and unconditional sequence. There are few to 
whom mere constancy of succession appears a sufficiently stringent 
bond of union for so peculiar a relation as that of cause and effect. 
Even if the reason repudiates, imagination retains, the feeling of 
some more intimate connection, of some peculiar tie, or mysterious 
constraint exercised by the antecedent over the consequent. Now 
this it is which, considered as applying to the human will, conflicts 
with our consciousness, and revolts our feelings. We are certain 
that, in the case of our volitions, there is not this mysterious 
constraint. We know that we are not compelled, as by a magical 
spell, to obey any particular motive. We feel, that if we wished 
to prove that we have the power of resisting the motive we could 
do so (that wish being, it needs scarcely be observed, a new 
antecedenf)^ and it would be humiliating to our pride, and paralyz- 
ing to our desire of excellence, if we thought otherwise. But 
neither is any such mysterious compulsion now supposed, by the 
best philosophical authorities, to be exercised by any cause over 
its effect. Those who think that causes draw their effects after 
them by a mystical tie, are right in believing that the relation 
between voHtions and their antecedents is of another nature. But 
they should go farther, and admit that this is also true of all other 
effects and their antecedents. If such a tie is considered to be 
involved in the word Necessity, the doctrine is not true of human 
actions ; but neither is it then true of inanimate objects. It would 
be more correct to say that matter is not bound by necessity, than 
that mind is so." ^ 

Mr. Mill escapes " the depressing effect of the fatalist 
doctrine " by saying that, while we must will as our 
character is, we can, if we desire, place ourselves in 
different circumstances, and these will work in us a 
different character, and then we shall will differently. 

1 Logic, pp. 581, 582. 



90 Inductive Logic. 

That is, our history having been what it has, we cannot 
will differently from what we do, but we can wish to 
will differently. But this is to suppose the same cause 
producing simultaneously a will in one direction and a 
wish in the other direction, — the same fountain send- 
ing forth sweet water and bitter. Mr. Mill says that 
"human actions are never ruled by any one motive 
with such absolute sway that there is no room for the 
influence of any other. The causes, therefore, on 
which an action depends are never uncontrollable." 
But it is precisely the characteristic of causation in 
physics that there is never an alternative unless some 
will intervenes. If human actions are never absolutely 
ruled by one motive, they differ from the reactions of 
matter, which are absolutely ruled in each case by one 
cause. 

The conviction made by a careful examination of 
Mr. Mill's doctrine of Causation is, that it lacks 
in clearness and self-consistency, and that it is 
an inadequate basis for the whole superstructure of 
Inductive Logic. 



CHAPTER XI. 
CANONS FOR ISOLATING FACTS OF CAUSATION. 

It is one task of Science, amid the crowd of phe- 
nomena, to distinguish between the coexistences ♦and 
successions which are accidental and those which rest 
upon real relations. For it is only by such knowledge 
that man can live among the terrific forces of nature 
and can make them the servants of his will. There 
are many groups of phenomena of which it may be 
known that when one is present, the others are present 
also. They are permanent coexistences. There are 
many events of which it may be known that when one 
has happened, the other or the others will be sure to 
follow. There is said to be a relation of causation 
between them. We have already, at great length, dis- 
cussed the word cause. An event is the reaction of 
certain substances and energies in a certain collocation. 
The reaction by which this collocation arose, or any 
previous reaction in the long line of history, is an his- 
torical cause of the event. This total of things, 
including the collocation, which is their mutual relation 
in space, and including their history in time, may be 
called the Comprehensive Cause of the event, and also 
of the things in their states after the event. ' 

Events are the actions of things. But every action 
is a reaction. This is a primary induction which men 
were long in making. The law of inertia, that every 
body remains in its state of rest or motion until acted 



g2 Inductive Logic. 

upon, is a subordinate generalization: the wider law is 
that it takes at least two to make, not only a bargain 
or a quarrel, but anything. This is often what is 
understood to be meant by the law of causation; and 
it seems to be regarded as intuitively known. But it 
is really an induction. 

If we can isolate two things so that we are sure 
that no third is present, and if then an event occurs, 
we are sure that it is a reaction between those two 
things. When a bit of glowing iron is lowered into a 
jar of oxygen and vivid combustion follows, we are 
sure that the iron and the oxygen are reacting; those 
two things are the sole material causes of the event. 
When a feather and a gold coin are supported in an 
exhausted receiver and then by the turn of a screw are 
left unsupported, we know that they are free from all 
particular influences and are reacting with the general 
mass of things as a whole : the fall therefore is caused 
by that reaction alone. This general reaction is called 
gravitation. 

It is plain that the presence of a third thing destroys 
the isolation and leaves us in doubt. The combustion 
of a bit of iron in common air, where nitrogen is 
present, could not be known, without investigation, to 
be a reaction of the iron and oxygen alone. It might 
be a mutual reaction of all three or a reaction of 
the iron and the nitrogen. But so crowded is the 
world with things, and so multitudinous are their 
reactions, that it is a rare good fortune to be able 
mechanically to separate a pair or a group of reagents. 
What cannot be done physically must be done in 
thought. We must make a mental elimination, or 



Cations for Isolating Facts of Causation. 93 

perhaps a series of eliminations, and thus discover the 
various reagents that enter into the comprehensive 
cause of any event that may be in question. These 
eliminations are made in thought by the process of 
subtraction. 

Canon First. 

FOR ISOLATING FACTS OF CAUSATION BY THE TEST OF 
DIFFERENCE. 

In any two instances^ the circumstances which are not 
common are the causes of the events which are not 
common. 

This brief and general language requires explanation. 
By an instance is meant any group of phenomena 
which may be under investigation. By a circumstance 
is meant a substance, an energy, a will, a collocation, 
or a previous event. Consequently the cause dis- 
covered may be the material cause, the energetic cause, 
the conditional cause, the volitional cause, or the his- 
torical cause — the mere occurrence of the possibility 
of the reaction of the efficient causes. What is dis- 
covered is far more likely to be merely one factor of 
one of these causes than to be the whole of it ; there- 
fore, to avoid the tediousness of constantly saying 
"at least a part of one of the causes," we will adopt 
the name Empirical Cause. The circumstance dis- 
covered by this method is what ordinary experience 
leads unscientific people to speak of as the cause; 
and this crude use of experience is what is called 
empiricism. 

The validity of this canon is obvious. Since events 
are the reactions of things, whatever is different in the 



94 Inductive Logic. 

events must come from differences in the things, or in 
their collocations, which afford the possibilities of 
reaction. But differences in collocation arise through 
events. Thus the whole of the differences in two 
groups of phenomena must be accounted for by the 
things, their collocations, and their history. Let us 
consider a concrete example. In a dark room some 
one touches a button, and immediately a brilliant 
illumination follows. There are here two instances, 
the room in darkness and the room illuminated. 
Viewed historically, the difference in circumstances is 
that the one instance includes the previous event of 
the touch of the button and the other does not. The 
touch of the button is therefore the historical cause of 
the illumination. But leaving out of view the history, 
it will be found that the two instances differ in the col- 
location of things. In the one case materials are so 
disposed that there is no continuous circuit for the 
electricity and in the other case there is a continuous 
circuit. Here is found the conditional cause. Fur- 
ther, the two instances differ, in that in one the 
electricity passes and in the other it does not ; hence 
we discover the energetic cause, which is the elec- 
tricity. By thus confining the attention successively 
to the history, the materials, the energy, or the con- 
ditions, the several kinds of cause may be elicited. 
Under this canon four cases may arise: — ^" 
Case I. On striking the balance between circum- 
stances and events in the two instances, a single 
circumstance and a single event may be left, hot com- 
mon to both instances. If so, that circumstance is 
manifestly the empirical cause of that event. If, for 



Canons for Isolating Facts of Causation. 95 

example, into a glass containing some dilute sulphuric 
acid a few bits of marble be dropped, vigorous ebul- 
lition will ensue. The glass containing the acid, as it 
was before the dropping in of the marble, constitutes 
one instance; the same glass containing the marble in 
addition to the acid constitutes the second instance. 
Historically viewed, the only difference is that the one 
instance includes the previous event of the dropping in 
of the bits of marble; this therefore is the historical 
cause. But viewed materially, the sole difference is in 
the bits of marble, which were absent at first and 
afterwards present. The marble is therefore the 
material cause of the ebullition. But it is only the 
empirical material cause; it is not the comprehensive 
material cause, for in that the acid is as important a 
factor as the marble. When there are a number of 
things present and a new factor is introduced, we can- 
not tell by a single application of the canon how many 
of them co-operate with that new factor in a new com- 
prehensive cause. 

Case 2. On striking the balance, a group of circum- 
stances and a group of events may be left not common 
to the two instances. If so, those circumstances are 
the empirical causes of those events, but which are the 
causes of which, can be ascertained only by a further 
application of the canon to simpler instances. For 
example, Daniel Webster left the paternal farm and, 
after spending four years in Dartmouth College, 
graduated as an accomplished orator. The two 
instances are Webster without education and without 
eloquence, and Webster after his college education, 
delivering some eloquent oration. The two instances 



96 Inductive Logic. 

differ in the group of circumstances constituting a 
college education. But this group is very complex, so 
that, while it is plain that among the circumstances 
are included the empirical causes of polished eloquence, 
it is not plain whether any particular circumstance, as 
the study of the Greek and Roman classics, was in 
any sense a cause. Indeed, it may have been a 
hindrance. 

Case J. On striking the balance, the difference may 
be found to be, that in the first instance there is more 
of one circumstance and more of one event than in the 
second instance. This case is but a variety of the 
first ; for an additional quantity is a new circumstance 
or a new event. For example, a youth ambitious for 
athletic honors may, by careful training, wonderfully 
increase his muscular strength. He has always taken 
some care of his health, and a little natural superiority 
may be that which awakens his ambition ; but with 
more care comes more power. Here the added care is 
a new circumstance and the addition of strength is a 
new event. 

Case /f.. On striking the balance, the difference may 
be found to be that in the first instance there is more 
of several circumstances and more of several events, 
the kinds remaining unchanged. This is merely a 
variety of Case 2 ; for the new quantities are new 
circumstances and new events. For example, after 
taking the Bachelor's degree, one may go on another 
year and take the Master's degree. He will become a 
more learned person, but we do not know any better 
than before, which of his studies have contributed to 
the group of results included in an education. 



Canons for Isolating Facts of Causation. 97 

These four cases may be expressed in symbols as 
follows : — 

I. ABC def 2. ABCD efgh 3. AABC ddef 4. AABCDD efghh 
BC ef BC fg ABC def ABCD efgh 

A d A D e h A d A D e h 

Let capital letters represent circumstances and 
small letters represent events. On striking the bal- 
ance in Case i, the single circumstance A and the 
single event d are found not common. Since what is 
not common in the events must be owing to what is 
not common in the circumstances, A must be the 
empirical cause of d. In Case 2, A and D are not 
common among the circumstances, and e and h are not 
common among the events. A and D include, there- 
fore, the causes of e and h; but which is the cause of 
which, or whether one is inert and the other is the 
cause of both events, we cannot say. We must find 
another instance presenting A without D before we 
can make a further isolation. Case 3 gives the same 
result as Case i, and Case 4 gives the same result 
as Case 2. 

In the first case, as soon as we find the instance 
ABC def, we know that those circumstances are the 
causes of those events; for, unless we are sure that 
there are no other significant circumstances and events, 
we have not found the instance at all. Just so, as 
soon as we find the instance BC ef, we know that 
those circumstances are the causes of those events. 
We make these affirmations on the basis of the primary 
induction that all of the events in the world are the 
reactions of things in the collocations which permit 
those reactions. Therefore we know that A, the 



98 Inductive Logic. 

circumstance in which the two instances differ, is the 
empirical cause of dy the event in which they differ. 
But it often happens that we can find no single 
instance BC ef, although we may know from previous 
observations that B is the cause of e and that C is the 
cause of /. This makes no difference in the reasoning 
or in the result. However the knowledge that B and 
C cause e and / has been obtained, we make the same 
use of it ; we subtract from the totals in the first in- 
stance those circumstances and events whose relations 
are already known, and the remaining circumstances 
and events are then known to be mutually related, or 
we know at least that among the circumstances are the 
causes of all the events not common. The same 
remark may be made mutatis mutandis of the three 
other cases. 

From the establishment of a single fact of causation 
we pass easily to a generalization. The primary 
inductions, that things persist, and that the qualities of 
things persist, are already made. What a thing causes 
once, it always causes under the same conditions. 
Therefore, after isolating a single fact of causation, we 
are warranted in the secondary induction, that the cir- 
cumstance, under the same conditions, will always 
cause the given event. 

The test of difference, when two good instances can 
be found or artificially produced, is quick and decisive. 
In the experiment of Count Rumford, it was easy to 
compare the apparatus when the water was cold and 
when the water was hot. It was easy also to see that 
the only circumstance in which the two instances 
differed was the motion of the cylinder. The event. 



Canons for Isolating Facts of Causation. 99 

the heating, was therefore undoubtedly attributable to 
that circumstance as empirical cause. But it is not 
always possible to apply this canon, and then our only 
resource is one far less satisfactory. 

Canon Second. 

FOR ISOLATING FACTS OF CAUSATION BY THE TEST OF 
A GREEMENT. 

If in two instances the same event occurs, the common 
circumstances probably include the cause ; and the proba- 
bility rapidly increases with the member and variety of 
the instances. 

The word cause here still means merely empirical 
cause. Inexact as this test is, it is often our only expe- 
dient, and with care it is highly useful. For example, if 
twice after the imposition of a protective tariff, business 
is seen to flourish, a slight probability arises that the 
tariff is the cause of the prosperity. Yet there is a 
possibility in each case that some other circumstance, 
as unusual harvests, or discoveries of rich deposits of 
the precious metals, may have been the cause. Indeed, 
the only effect of the tariff may have been to diminish 
somewhat each time the total prosperity. But every 
instance in which a tariff is accompanied by prosperity 
rapidly increases the probability of a genetic connec- 
tion ; since otherwise we must suppose the fortuitous 
occurrence of some other beneficent cause every time 
Congress happens to be in favor of protection. 

The argument from the test of agreement often 
seems stronger than it is, from our unconsciously 
blending it with the argument from the test of differ- 



lOO IndtLctive Logic. 

ence. In the case of prosperity after the imposition of 
a tariff, we naturally compare the country as it was 
before the tariff and as it was soon after, and thus 
apply the test of difference ; but this gives to the argu- 
ment from agreement an appearance of strength not 
its own. 

It must be observed that, in the canon, the common 
circumstances are said simply to include, not necessa- 
rily all to be, the cause. The ashes of seaweeds were 
long known to possess valuable medicinal powers. 
The use of them in certain diseases was followed by 
beneficial effects. But it was not known which of the 
ingredients was efficient or whether all were efficient ; 
all were common circumstances, but some might be 
always inert, and some might even be obstructive. 
Later it was discovered that the useful substance was 
nothing but iodine ; the other things were better away. 

As an illustration of how the test of agreement may 
be applied, with some admixture of the test of differ- 
ence, we will quote an eloquent passage from Schiller's 
y^sthetical Essays : — 

" It is certainly a matter entitled to reflection that, at almost 
all the periods of history when art flourished and taste held sway, 
humanity is found in a state of decline ; nor can a single instance 
be cited of the union of a large diffusion of aesthetic culture with 
political liberty and social virtue, of fine manners associated with 
good morals, and of politeness fraternizing with truth and loyalty 
of character and life. As long as Athens and Sparta preserved 
their independence, and as long as their institutions were based 
on respect for the laws, taste did not reach its maturity, art 
remained in its infancy, and beauty was far from exercising her 
empire over minds. No doubt, poetry had already taken a 
sublime flight, but it was on the wings of genius, and we know 



Canons for Isolating Facts of Causation. loi 

that genius borders very closely on savage coarseness, that it is a 
light which shines readily in the midst of darkness, and which, 
therefore, often argues against, rather than in favor of, the taste of 
the time. When the golden age of art appears under Pericles and 
Alexander, and the sway of taste becomes more general, strength 
and liberty have abandoned Greece ; eloquence corrupts the truth, 
wisdom offends it on the lips of Socrates, and virtue in the life of 
Phocion. It is well known that the Romans had to exhaust their 
energies in civil wars, and, corrupted by Oriental luxury, to bow 
their heads under the yoke of a foreign despot, before Grecian art 
triumphed over the stiffness of their character. The same was the 
case with the Arabs : civihzation only dawned upon them when 
the vigor of their military spirit became softened under the 
Abbassides. Art did not appear in modern Italy till the glorious 
Lombard league was dissolved, Florence submitting to the Medici, 
and all those brave cities gave up the spirit of independence for 
an inglorious resignation. It is almost superfluous to call to 
mind the example of modern nations, with whom refinement has 
increased in direct proportion to the decline of their liberties. 
Wherever we direct our eyes in past times, we see taste and free- 
dom mutually avoiding each other. Everywhere we see that the 
beautiful only founds its sway on the ruins of heroic virtues." ^ 

Under this canon three cases may arise, represented 
by symbols as follows : — 

I. ABC def 2. ABC def 3. ABC def 

APE dgh ABE deg AFG deh 

A d AB de A de 

In the first case there is one common event and one 
common circumstance. In the second case there is a 
group of common events and a group of common cir- 
cumstances. In the third case there is a single 
common circumstance but a group of common events. 

This third case suggests a remark, vi^hich should be 
made also regarding the others. A serious element of 

^ Bohn's Trans., p. 55. 



102 Inductive Logic. 

uncertainty weakens the test of agreement, and that is 
what is called the Plurality of Causes. What is appar- 
ently the same event may be caused by different 
things. Light -may be made by electricity or by com- 
bustion. The canon asserts no more than that the 
common circumstances probably include the cause. 
Even in Case i, A^ the only common circumstance, 
may not be the cause of </, the only common event ; 
for B may be the cause of d in the first instance and D 
may be the cause of d in the second. A may be wholly 
inert in both instances. It is only when a number of 
instances have been observed that confidence finds 
much basis. Ebullition may occur in hydrochloric 
acid, and yet all the common circumstances may be 
irrelevant, for marble may be the cause in one instance 
and zinc may be the cause in the second. In Case 3, 
A may be the cause of d and some other circumstance 
may each time cause e. 



CHAPTER XII. 

MR. MILL'S FOUR EXPERIMENTAL METHODS. 

To Mr. Mill is due the credit of first distinctly 
formulating and elaborately discussing the methods of 
isolating facts of causation. His treatment of the sub- 
ject has powerfully influenced all subsequent writers, 
and his terminology has entered into the general 
vocabulary of philosophy. It is, therefore, necessary 
for the student to understand these, if he would under- 
stand the current literature of inductive logic. 

Mr. Mill treats of the tests which we have discussed 
in the last chapter, under the heading, " The Four 
Experimental Methods." He recognizes, indeed, that 
fundamentally there are but two, and says : — 

" The simplest and most obvious modes of singling out from 
among the circumstances which precede or follow a phenomenon, 
those with which it is really connected by an invariable law, are 
two in number. One is, by comparing together different instances 
in which the phenomenon occurs. The other is, by comparing 
instances in which the phenomenon does occur, with instances in 
other respects similar in which it does not. These two methods 
may respectively be denominated the Method of Agreement and 
the Method of Difference." i 

For the application of these methods Mr. Mill pro- 
ceeds to formulate five canons, as follows : — 

1 Logic, p. 278. 



104 Inductive Logic. 

First Canon. 

For the Method of Agreement, 

If two or more instances of the phenomenon under investiga- 
tion have only one circumstance in common, the circumstance in 
which alone all the instances agree, is the cause (or effect) of the 
given phenomenon. 

Second Canon. 

For the Method of Difference. 

If an instance in which the phenomenon under investigation 
occurs, and an instance in which it does not occur, have every 
circumstance in common save one, that one occurring only in the 
former ; the circumstance in which alone the two instances differ, 
is the effect, or the cause, or an indispensable part of the cause, 
of the phenomenon. 

Third Canon. 

For the foint Method of Agree7nent and Difference; or the 
Indirect Method of Difference. 

If two or more instances in which the phenomenon occurs have 
only one circumstance in common, while two or more instances in 
which it does not occur have nothing in common save the absence 
of that circumstance ; the circumstance in which alone the two 
sets of instances differ, is the effect, or cause, or an indispensable 
part of the cause, of the phenomenon. 

Fourth Canon. 

For the Method of Residues. 

Subduct from any phenomenon such part as is known by previ- 
ous inductions to be the effect of certain antecedents, and the 
residue of the phenomenon is the effect of the remaining antece- 
dents. 



Mr. Mill's Four Experhnental Methods. 105 

Fifth Canon. 
For the Method of Conco7niiant Variations. 

Whatever phenomenon varies in any manner whenever another 
phenomenon varies in some particular manner, is either a cause or 
an effect of that phenomenon, or is connected with it through 
some fact of causation. ' 

vUpon these methods we remark : — 

I. The name "The Four Experimental Methods" 
is of doubtful propriety. The methods are confessedly 
in principle but two ; and the canons are five. But 
Mr. Mill fixed upon the number four because he did 
not regard the method of Residues as strictly inductive. 
The method of Residues provides for those instances 
of the application of the method of Difference which 
we have discussed under Case i of our Canon i, on 
page 98, in which, instead of subtracting a single 
instance, we subtract the sum of several instances, in 
order to make the isolation. The fact that in such 
cases the subtrahend is composite, made by an addition 
of simpler instances, leads Mr. Mill to formulate a 
special canon and to declare it deductive. He is not 
always of the same mind regarding the method of 
Residues ; since he says, " By previous inductions we 
have ascertained the causes of some of these effects," ^ 
meaning those which are added together to make the 
compound subtrahend ; but he says later, " It concludes 
not from a comparison of instances, but from the 
comparison of an instance with the result of a previous 
deduction.'" ^ 

1 Logic, p. 284. 2 /bid,^ p. 613. 



io6 Inductive Logic. 

The method of Residues and the method of Differ- 
ence are, however, identical in principle. The rare 
word "subduct," which Mr. Mill employs, means only 
"take .the difference," and a "residue" is nothing but 
a "difference." The single step of addition cannot 

make the difference between induction and deduction. 

i 

Mr. Mill says, " The Method of Residues is in truth a 
peculiar modification of the Method of Difference," 
and again, " The Method of Residues, as we have seen, 
is not independent of deduction ; though, as it also 
requires specific experience, it may, without impro- 
priety, be included among methods of direct observation 
and experiment." This remark implies that Mr. Mill 
regarded the other methods as entirely independent of 
deduction. Still he says . of the two fundamental 
methods, "Both are methods of elimination." But 
elimination is a purely deductive process. Mr. Mill 
did not see that deductive logic covers the whole field 
of induction, that his methods only served to isolate 
single facts, and that he then combined those facts, 
directly in making a primary induction, or in a syllogism 
with some primary induction already made, to get some 
general truth as a secondary induction. He has told 
us these things in detached portions with great clear- 
ness, but he never put them together. Mr. Mill seems 
to think that his methods give us general truths 
immediately. But facts isolated by these methods 
have no more inductive significance than other single 
facts which need no artificial isolation. 

In attempting to use the test of difference, we may 
discover that we have not accurately stated our 
instances. For example, we may think that we have 



Mr. Mill's Four Experimental Methods. loy 

observed the two instances BC def and BC ef. 
But upon comparison it appears that while the causes 
observed in both instances are the same, there is an 
effect in one which is not in the other. This shows 
that we must have overlooked a cause, and puts us 
upon a search for it. Mr. Mill sometimes seems to 
regard this correction of instances as a use of the 
method of residues. He quotes with approval the 
language of Whewell, " Many of the new elements of 
chemistry have been detected in the investigation of 
residual phenomena. Thus Arfwedson discovered 
lithia by perceiving an excess of weight in the sulphate 
produced from a small portion of what he considered 
as magnesia present in a mineral he had analyzed." 
But this correction of instances is just as likely to 
occur in using the simple method of difference as in 
using the method of residues. There is no necessary 
connection between the correction of instances and 
the use of a compound subtrahend, which is the char- 
acteristic of the method of residues. 

The term " experimental " is even less defensible 
than the number four. For Mr. Mill says : " Of these 
methods, that of Difference is more particularly a 
method of experiment ; while that of Agreement is 
more especially the resource employed where experi- 
ment is impossible." If it is employed especially 
where experiment is impossible, some name should be 
found more appropriate than " experimental." 

2. Mr. Mill does not seem aware of the vagueness 
of the terms and results of his canons. In his chapter 
on the Law of Causation, he says, "The cause then, 
philosophically speaking, is the sum total of the condi- 



io8 Inductive Logic, 

tions positive and negative taken together, the whole 
of the contingencies of every description, which being 
realized, the consequent invariably follows." But the 
methods never isolate a cause in this sense ; it is only 
the empirical cause — some single factor or group of 
factors. It is, therefore, superfluous to say in the 
second and third canons " the cause or an indispensable 
part of the cause." 

Mr. Mill regarded succession as essential in the 
notion of causation, and, illustrating the methods by 
letters of the alphabet, he says, "We shall denote 
antecedents by large letters of the alphabet, and the 
consequents corresponding to them by the small." 
Yet in only one of the canons does he make any refer- 
ence to sequence. Indeed, he makes them so general 
that the conclusion may be that the "circumstance" 
is either the cause or the effect of the phenomenon. 
This failure to hold fast the idea of sequence leads to 
curious results. Take the following illustration of the 
method of agreement : — 

" For example, let the effect a be crystallization. We compare 
instances in which bodies are known to assume crystalline struc- 
ture, but which have no other point of agreement ; and we find 
them to have one, and as far as we can observe, only one, 
antecedent in common : the deposition of a solid matter from a 
liquid state, either a state of fusion or of solution. We conclude 
therefore, that the solidification of a substance from a liquid state 
is an invariable antecedent of its crystallization." ^ 

It is impossible here to detect any succession. A 
substance does not first solidify, and then crystallize. 
What has been discovered, if anything, is not a fact of 
succession, but one of coexistence. 

1 Logic, p. 279. 



Mr. Mill's Four Experimental Methods. 109 

But in what sense is solidification the cause of 
crystallization ? It is not the material cause ; the 
sugar, alum, or other substance is the material cause. 
It is not the energetic cause ; that is some peculiar 
kind of cohesion. It is not the historical cause ; for 
the event solidification does not precede the event 
crystallization. Solidification is not the " uncon- 
ditional, invariable antecedent " of crystallization, for 
many substances solidify without crystallizing. All 
that the investigation has shown is, that if materials 
take the forms of regular solids, they assume regularity 
when they assume solidity. We have discovered not a 
noun or a verb, but an adverb ; the time of solidifying 
is the time of regularly solidifying. 

Mr. Mill seems never to have considered whether, in 
a sentence, "the cause" is the noun or the verb or 
some other part of speech. If " Cain killed Abel," was 
Cain the cause of Abel's death, or was the "killing" 
the cause } Was it the arrival of Bliicher at Waterloo 
that caused the defeat of Napoleon, or was it Bliicher 
himself.'^ 

3. Mr. Mill's joint method of Agreement and Differ- 
ence is wholly an illusion. There is no such method 
known to science. The discovery of several instances 
agreeing in nothing has no probative force whatever. 
If twice after eating lobster I have been ill, the belief 
that the lobster was the cause of the illness receives 
no particle of support from the facts that a concave 
lens disperses light, and that the Turks captured Con- 
stantinople. 

Dr. Fowler saw that Mr. Mill's statement was defec- 
tive, and added the condition that the negative instances 



no Inductive Logic, 

must be "within the same department of investiga- 
tion," that is, they must be good enough for use 
according to the single method of difference. It is, 
indeed, often possible to prove a fact independently, 
both by the test of agreement and by the test of dif- 
ference ; but the combination of these two independ- 
ently sufficient proofs is not at all what Mr. Mill 
means by his joint method. In the observations upon 
the cause of dew, which Mr. Mill and Dr. Fowler use 
as an illustration of the double rhethod, it was first 
shown, by a primary induction, that all bodies upon 
which dew is deposited agree either in losing heat 
rapidly or in conducting it slowly, that is they have a 
lower temperature than the air ; then the universal 
negative was admitted, that dew is never found on any 
other bodies ; and then it was inferred that the property 
of being cooler than the surrounding air was the sole 
cause of dew. It is obvious that this was something 
very different from finding two instances of agreement 
and two instances agreeing in nothing. Mr. Mill 
says : — 

"It thus appears that the instances in which much dew is 
deposited, which are very various, agree in this, and, so far as we 
are able to observe, in this only, that they either radiate heat 
rapidly or conduct it slowly : qualities between which there is no 
other circumstance of agreement than that by virtue of either, the 
body tends to lose heat from the surface more rapidly than it can 
be restored from within. The instances, on the contrary, in 
which no dew, or but a small quantity of it, is formed, and which 
are also extremely various, agree (as far as we can observe) in 
nothing except in not having this same property. We seem, 
therefore, to have detected the characteristic difference between 
the substances on which dew is produced and those on which it is 



Mr. Mill's Four Experimental Methods. iii 

not produced. And thus have been reahzed the requisitions of 
what we have termed the Indirect Method of Difference, or the 
Joint Method of Agreement and Difference." ^ 

Here several things are confused. The pure method 
of difference was employed in showing that bodies with 
dew differed from those without dew simply in being 
colder than the air. An exhaustive examination estab- 
lished the general negative that dew occurs nowhere 
else ; but this proves, not that coldness is the cause of 
dew, but that there is no other cause. Suppose that 
the question had been of heating caused by friction. 
Two cases agreeing only in the circumstance friction, 
and in the event heating, would meet the requirements 
of the first part of the canon ; but we cannot prove 
the universal negative that heating never occurs without 
friction, and it is inconceivable that any confirmation 
could be found in the properties of lenses, or the fall of 
Constantinople. 

Dr. Fowler added to Mr. Mill's canon the words : 
" Moreover (supposing the requirements of the Method 
to be rigorously fulfilled), the circumstance proved by 
the method to be the cause is the only cause of the 
phenomenon." He does not tell us how the require- 
ment of finding "two or more instances from which 
the phenomenon is absent " can be rigorously fulfilled, 
but a little reflection will show that it is by proving a 
universal negative ; this, certainly, is rigor in finding 
"two or more " negative instances. 

4. The Method of Concomitant Variations, which 
corresponds to our Cases 3 and 4 under Canon i, is 
used upon some very interesting facts, but logically 

1 Logic, p. 299. 



112 Inductive Logic. 

has no distinctness from the ordinary method of differ- 
ence. Nor does the language need to be so elastic. 
The cases in which the consequent seems to decrease 
when the antecedent increases are only verbally different 
from those in which both increase together. All can be 
stated in terms of increase. For instance, instead of 
saying "the more heat the less condensation," we may 
say "the more expansion." Each pair of instances of 
concomitant variation affords a complete opportunity 
for the regular application of the test of difference, and 
the other pairs of cases, which are innumerable, simply 
enable us to proceed at once to a primary induction. 

5. Mr. Mill seems to have exaggerated, with paternal 
partiality, the importance of these methods, which he 
had formulated and named and presented to the philo- 
sophical world. He says : — 

"The four methods which it has now been attempted to 
describe, are the only possible modes of experimental inquiry — 
of direct induction a posteriori^ as distinguished from deduction; 
at least I know not, nor am able to imagine any others. And 
even of these, the Method of Residues, as we have seen, is not 
independent of deduction ; though, as it also requires specific 
experience, it may, without impropriety, be included among 
methods of direct observation and experiment. These then, with 
such assistance as can be obtained from deduction, compose the 
available resources of the human mind for ascertaining the laws 
of the succession of phenomena." 1 

According to this, the whole of Induction is concerned 
with facts of causation ; no place is reserved for facts 
of coexistence or of likeness, or for the inductions 
built upon them. Nor, indeed, is any explicit provision 

1 Logic, p. 291. 



Mr. Mill 'i- Four Experimental Methods. 113 

made for constructing inductions of any kind out of 
facts. But the facts isolated by these tests must be 
treated by the mind just hke any other data of observa- 
tion. They are not inductions, but must be generalized 
into primary inductions, or syllogized into secondary or 
mixed inductions, if they are to teach us anything. 
The test of difference gives immediate certainty, each 
time, regarding one solitary fact of causation. The test 
of agreement gives, upon the comparison of the first 
two instances, only a slight presumption of one fact of 
causation, but this slight probability, upon the compar- 
ison of more instances, gradually strengthens into a 
primary induction of a causal connection in all the 
instances. It should not be forgotten that no general 
truth can ever be reached in inductive logic except by 
a primary induction, directly used, or applied as one of 
the premises of a syllogism. Mr. Mill seems to think 
that all of the inductive thought of antiquity was 
simple enumeration, and that the use of the methods is 
the characteristic of modern science. He speaks of 
" the ancients with their inductio per enumerationein 
simplicem,'' somewhat contemptuously. But, of course, 
the ancients isolated facts, by the methods of agreement 
and of difference, every hour of their lives ; for they 
could not make primary inductions without isolating 
facts. The thinking of the ancients was inexact, but 
they were not unaccustomed to any fundamental opera- 
tion of the mind. The characteristic difference between 
their thinking and ours cannot be, that we have sub- 
stituted precision in isolating facts, for rashness in 
generalizing ; the two things are not in the same 
plane. It is impossible to avoid the belief that what 



114 Inductive Logic. 

led Mr. Mill to regard the methods as so much more 
scientific than inductio per e^iumerationem simplicem 
was the deductive process, involved in making a secon- 
dary induction, which he immediately performed after 
isolating a single fact of causation, and by which he 
reached at once a trustworthy generalization. 



CHAPTER XIII. 



HYPOTHESIS. 



Whenever we meet with a disconnected fact, the 
mind instinctively seeks to refer it to some place 
in the general order. An Hypothesis is a conjec- 
ture made to account for some unexplained fact or 
facts. To account for a fact is to refer it to some 
uniformity or conjunction of uniformities. To speak 
then more exactly, an Hypothesis is the reference of a 
fact to a uniformity or a conjunction of uniformities, 
before we have evidence enough to feel sure about it. 
The word Theory is often used as synonymous with 
hypothesis ; but it would be better to call the reference 
an hypothesis before we feel sure of its truth, and a 
theory after we become sure. 

There is no other way to account for facts, except to 
refer them to uniformities. For the uniformities them- 
selves, no reason can be given. The mind is satisfied 
with them as finalities. If one asks. Why is that bird 
black } and is answered, That is a crow and all crows 
are black, he accepts that answer as sufficient. Or if, 
being a chemist, he is led to ask. What pigment makes 
the crow's feathers black.? when he finds the presence 
of a certain substance which is always black, he is 
satisfied. Newton asks why that apple falls, and 
having generalized that all things fall towards each 
other, is glorified as having explained the fall of the 
apple. 



Ii6 Inductive Logic. 

Writers upon inductive logic often please themselves 
with the notion that they are looking deeper into 
nature than its uniformities ; but this is a delusion. 
Professor Minto says : — 

"Science aims at reaching 'the causes of things': it tries to 
penetrate behind observed uniformities to the explanation of them. 
In fact, as long as a science consists only of observed uniformi- 
ties, as long as it is in the empirical stage, it is a science only by 
courtesy. Astronomy was in this stage before the discovery of 
the Law of Gravitation. Medicine is merely empirical as long as 
its practice rests upon such generalizations as that Quinine cures 
ague, without knowing why. It is true that this explanation may 
consist only in the discovery of a higher or a deeper uniformity, 
a more recondite law of connection : the point is that these deeper 
laws are not always open to observation, and that the method of 
reaching them is not merely observing and recording." i 

It would be much clearer to say simply that science 
aims to discover the highest and deepest uniformities, 
and is not satisfied until it has analyzed the so-called 
■^empirical laws," that is, the uniformities which arise 
from the co-operation of simpler ones, into their factors. 
The " Laws of Nature " are merely the uniformities of 
the resemblances, coexistences, and reactions of things. 
No uniformity of any kind is open to observation in 
the sense that it can be known by simply observing 
and recording, without a mental process. The methods 
of discovering the deeper uniformities differ in no way 
from those used in discovering the empirical ones, nor 
is there any line which marks the boundary between 
the more and less complex uniformities. 

Every person is constantly making hypotheses. 
Every sensation that comes to the mind challenges an 

1 Logic, p. 268. 



Hypothesis. 117 

explanation. It demands to be in some way classified, 
and refuses to give us rest until disposed of. The 
ordinary course is to refer the new phenomenon at 
once to some known uniformity, but often most mis- 
takenly. An amusing illustration occurs in the Life 
and Letters of Charles Darwin : — 

" When at Cambridge I used to practice throwing up my gun 
to my shoulder before a looking-glass to see that I threw it up 
straight. Another and better plan was to get a friend to wave 
about a lighted candle, and then to fire at it with a cap on the 
nipple, and if the aim was accurate the little puff of air would 
blow out the candle. The explosion of the cap caused a sharp 
crack, and I was told that the tutor of the college remarked, 
"■ What an extraordinary thing it is, Mr. Darwin seems to spend 
hours in cracking a horse-whip in his room, for I often hear the 
crack when I pass under his window.' " ^ 

The tutor formed an hypothesis ; he referred the 
sound which he heard to the uniformity which, among 
those that he knew, it most resembled. 

Since, in the production of any event, a large number 
of uniformities frequently coincide, most hypotheses 
are somewhat complex, but their essential nature is the 
same. 

No criterion can be fixed by which it may be decided 
when the reference of a fact to a uniformity passes 
from the condition of an hypothesis to that of an 
induction. When the mind is satisfied that there is 
proof enough, the hypothesis becomes an induction. 
This point will be reached much more readily by some 
minds than by others. Professor Huxley regarded the 
opinion that modern horses are descended from small 

1 Page 31. 



Ii8 Inductive Logic. 

five-toed progenitors as "demonstratively established," 
while many others still looked upon evolution as a very 
slenderly supported hypothesis. 
An Hypothesis is legitimate: — 

1. When it includes all the known facts in the case. 

2. When it is the simplest that has been suggested. 

3. When the supposed phenomena fall into the lines 
of known uniformities. 

This third requirement is, we believe, what Sir 
Isaac Newton meant by laying down the rule that the 
hypothesis must assign a vera catcsa, a true cause. He 
could not have meant that no new cause must be 
assumed, for the very purpose of hypothesis is to deal 
with new things. He could not have meant that the 
cause assumed must be the r^<^/ cause; for that would 
have been a foolish truism. He must have meant 
that the assumed uniformity was to be of a kind 
already known to exist. For example, if an explosion 
occurs in a flouring mill, we may adopt the hypothesis 
that it was caused by the fine, floating dust of flour, in 
sudden combustion. Many substances have the prop- 
erty of explosive combustion ; this is a vera causa. If 
flour has this property, it but adds one more in an 
already established line of uniformity. But should we 
assume that the explosion was caused by ghosts, this 
would not be in line with what is known to happen in 
other cases ; we should have not only a new cause, but 
a new kind of cause. 

An hypothesis is illegitimate when it violates any 
one of the foregoing rules. It is gratuitous when it 
violates the second rule, or when there are no unex- 
plained facts to start with. It is irrational to make a 



Hypothesis. 119 

gratuitous hypothesis, for inductive science cannot let 
go of facts. 

Mr. Mill's definition is as follows: — 

" An hypothesis is any supposition which we make (either with- 
out actual evidence, or upon evidence avowedly insufficient), in 
order to endeavor to deduce from it conclusions in accordance 
with facts which are known to be real ; under the idea that, if the 
conclusions to which the hypothesis leads are known truths, the 
hypothesis itself either must be, or at least is likely to be, true." ^ 

Mr. Mill lays it down as a condition of a genuinely 
scientific hypothesis, "that it be not destined always 
to remain an hypothesis, but be certain to be either 
proved or disproved by that comparison with observed 
facts which is termed verification." This condition we 
cannot accept ; the mind is impelled to account for the 
phenomena about it in the simplest and most harmo- 
nious manner possible, and the question of expectation 
for the future is wholly irrelevant. The hypothesis 
that a certain ship that sailed away from port and 
never was heard from again, ran into an iceberg, is 
perfectly legitimate, if it accounts for all the facts, is 
the simplest suggested, and is in line with what hap- 
pens in that part of the ocean. Whether we expect 
to find hereafter some of the wreckage, it is not neces- 
sary to consider. 

The right use of hypothesis was well illustrated in 
the discovery of the planet Neptune. For some time 
it had been observed, that the orbit of the planet 
Uranus was subject to an amount of perturbation 
which could not be accounted for from the influence of 
known planets. 

1 Logic, p. 349. 



I20 Inductive Log-ic. 



ii 



" Of the various hypotheses formed to account for it [the per- 
turbation], during the progress of its development, none seemed 
to have any degree of rational probability but that of the exist- 
ence of an exterior, and hitherto undiscovered, planet, disturbing, 
according to the received laws of planetary disturbance, the 
motion of Uranus by its attraction, or rather superposing its dis- 
turbance on those produced by Jupiter and Saturn, the other two 
of the old planets which exercise any sensible disturbing action on 
that planet. Accordingly, this was the explanation which natu- 
rally, and almost of necessity, suggested itself to those conversant 
with the planetary perturbations who considered the subject with 
any degree of attention. The idea, however, of setting out from 
the observed anomalous deviations, and employing them as data 
to ascertain the distance and situation of the unknown body, or, 
in other words, to resolve the inverse problem of perturbations, 
'given the disturbances, to find the orbit and the place in that 
orbit of the disturbing planet,' appears to have occurred only to 
two mathematicians, Mr. Adams in England and M. Leverrier in 
France, with sufficient distinctness and hopefulness of success to 
induce them to attempt its solution. Both succeeded, and their 
solutions, arrived at with perfect independence, and by each in 
entire ignorance of the other's attempt, were found to agree in a 
surprising manner when the nature and difiiculty of the problem 
is considered ; the calculations of M. Leverrier assigning for the 
heliocentric longitude of the disturbing planet for the 23rd Sept., 
1846, 326° o', and those of Mr. Adams (brought to the same date) 
329° 19', differing only 3° 19'; the plane of its orbit deviating very 
slightly, if at all, from that of the ecliptic. 

"On the day above mentioned — a day forever memorable in 
the annals of Astronomy — Dr. Galle, one of the astronomers 
of the Royal Observatory at Berlin, received a letter from M. 
Leverrier, announcing to him the result he had arrived at, and 
requesting him to look for the disturbing planet in or near the 
place assigned by his calculation. He did so, and on that very 
night actually found it. A star of the eighth magnitude was seen 
by him and by M. Encke in a situation where no star was marked 
as existing in Dr. Bremiker's chart, then recently published by the 
Berlin Academy. The next night it was found to have moved 



Hypothesis. 121 

from its place, and was therefore assuredly a planet. Subsequent 
observations and calculations have fully demonstrated this planet, 
to which the name of Neptune has been assigned, to be really 
that body to whose disturbing attraction, according to the New- 
tonian law of gravity, the observed anomalies in the motion of 
Uranus were owing.^ 

The manner in which scientific men construct theo- 
ries may be illustrated by Darwin's conjectures as to 
the formation of coral islands : — 

" Stibsidence Theory of Darwin. — This theory explains not 
only atolls, but also barriers, and connects both in a satisfactory 
manner with fringing reefs. It supposes that the sea-bottom, 
where atolls and barriers occur, has been for ages subsiding, but 
at a rate not greater than the upward building of the coral-ground ; 
that every reef commences as a fringing reef, but, in the progress 
of subsidence, was converted first into a barrier and finally into 
an atoll. For, as the volcanic island went down, the corals would 
build upward on the same spot ; and as the island would become 
smaller and smaller, and the corals would grow faster on the outer 
side of the reef, where they are exposed to the breakers, it is evi- 
dent that the reef would become separated from the island by a 
ship-channel, and thus become a barrier. Finally, when the island 
disappears entirely, the reef, still building upward, would become 
an atoll. ... It is seen that the corals do not build a vertical 
wall, and therefore that the atoll is always smaller than the coast- 
line of the original island. Consequently, if the subsidence 
continues, a typical atoll is changed into a small, closed lagoon, 
and, finally, into a lagoonless island. These, therefore, indicate 
the deepest subsidence, 

'■'•Evidences. — i. This theory accounts for all the more obvious 
phenomena of atolls, such as their irregular circular form, their 
size, the steepness of their outer slopes, etc. 2. Every stage of 
gradation between the fringing reef on the one hand, and the atoll 
on the other, has been traced by Dana, strongly suggesting that 

1 Herschel's Outlines of Astronomy, fourth ed., §§ 767, 768, quoted 
by Fowler, Inductive Logic, pp. 177, I'jZ. 



122 Inductive Logic, 

they are all different stages of development of the same thing. 
We have in the Pacific some high islands, which are surrounded 
by a pure fringing reef ; others in which the reef is a fringe on 
one side and a barrier on the other ; others in which the barrier 
is one mile, two miles, five miles, ten miles, twenty, or thirty miles 
distant ; others which are called atolls, but the point of the 
original volcanic island is still visible in the middle of the lagoon ; 
others which are perfect atolls, but, by sounding, the head of the 
drowned volcanic island is still detectable. The next .step in the 
series is the perfect atoll, then the small atoll, and, finally, the 
lagoonless coral island. These last kinds show that the original 
island has gone down deeply. 3. By grappling-hooks ^<?^^ coral- 
trees have been broken off and brought up from the ground 
where they once grew, now far below the limiting depth of coral 
growth. The evidence of subsidence in this case is of the same 
kind and force as that derived from submerged forest-ground. 
The corals have been carried below their depth and drowned. 4. 
The remarkable distribution of the various kinds of reefs brought 
to light by Dana is satisfactorily explained by this theory, and 
therefore is an argument in its favor. In the middle of the atoll 
region of the Pacific there is a blank area^ 2000 miles long and 
1000 or more miles wide, where there are no islands. Next 
about this is an area in which small atolls predominate ; about 
this again the region of ordinary atolls ; beyond this the region 
mostly of barriers, and finally of fringes. Now, by this theory 
this distribution is thus explained : The sea-bottom in the blank 
area has gone down so fast that the corals have not been able to 
keep pace, and have therefore been drowned, and left no monu- 
ment of their existence. In the next region the corals have been 
able to keep within living distance of the surface, but the original 
islands have not only disappeared, but gone down to great depths. 
In the next the original high islands have disappeared, but not 
gone down so deep ; in the next they have sunk only to the mid- 
dle. The fringing reefs stand on the margin of the sinking area. 
Outside of this again there is in some places even evidence of 
upheaval instead of subsidence. Raised beaches in the form of 
fringing-reef rocks are found clinging to the sides of high islands 
many feet above the present searlevel. 5. In some places this 



Hypothesis. 123 

subsidence seems to be still in progress. On certain coral islands 
sacred structures of stone made by the natives are now standing 
in water, and the paths worn by the feet of devotees are now 
passages for canoes (Dana)." 

^^ Murray's Theory. — Recently serious doubts have been cast 
on Darwin's subsidence theory, at least as a universal explanation 
of barriers and atolls. Mr. Murray, from his observations during 
the voyage of the Challenger^ believes that barriers and atolls may 
be explained without subsidence of the sea-floor. An outline of 
his views may be thus stated: (i) Submarine banks formed in 
any way, either {a) built up by accumulating shells of successive 
generations of marine animals, until within the reach of coral 
growth ; or {b^ by volcanic cinder cones cut down by the waves 
so as to form suitable banks. (2) The banks taken possession of 
by corals are built up to the sea-level. (3) The coral growth is 
confined, or at least most rapid, on the outer margin, because 
exposed to the action of the sea. Thus arises a ring with blank 
space within. (4) The action of waves beats these rings into a 
series of islets. (5) Meanwhile the scouring action of currents 
and the solvent action of sea-water scoops out the blank area into 
a more or less deep lagoon. (6) The action of waves breaking 
the living coral and the reef-rock forms a debris-^^^ or talus, with 
steep outward slope, on which the corals continue to grow sea- 
ward into deep water. Thus the coral ring continues to spread, 
like 2. fairy ring, by growing seaward in every direction, and dying 
behind. (7) According to Darwin, atolls grow continually smaller; 
according to Murray, they grow continually larger. 

" Barriers are similarly explained. They commence as fringes, 
which grow seaward as far as depth will allow. Then the corals 
die near the shore, and this part is scoured out into a channel. 
Meanwhile the reef extends seaward on its own talus, and the 
channel is pari passu widened. 

" In the present condition of the question it is probable that 
there are more ways than one in which barriers and atolls may be 
formed, but Darwin's view seems still to hold its own as a general, 
though not as a universal theory." ^ 

1 Le Conte's Geology, pp. 150-153. 



124 Inductive Logic. 

The formation of wise hypotheses is the most impor- 
tant step in the progress of science. It is simply 
suspecting the lines of nature's uniformity from slight 
hints. The fundamental preparation for it is intimate 
familiarity with the general system of things, so far as 
discovered. Helmholtz has well stated the case in the 
following passages. It will be observed that instead 
of "foreknowledge" it would have been better to use a 
more general word. Induction has as much to do with 
the past, the distant, and the unobservable present, as 
it has to do with the future. It deals with all of these 
not as past, present, and future, but as unseen parts of 
the existing order ; it is able to reason about them only 
as parts of that order. 

" In order to acquire this foreknowledge of what is coming, but 
of what has not been settled by observations, no other method is 
possible than that of endeavoring to arrive at the laws of facts by 
observations ; and we can only learn them by induction, by the 
careful selection, collation, and observation of those cases which 
fall under the law. When we fancy that we have arrived at a law, 
the business of deduction commences. It is then our duty to 
develop the consequences of our law as completely as may be, but 
in the first place only to apply to them the test of experience, so 
far as they can be tested, and then decide by this test whether the 
law holds, and to what extent. This is a test which really never 
ceases. The true natural philosopher reflects at each new phe- 
nomenon, whether the best established laws of the best known 
forces may not experience a change ; it can, of course, only be a 
question of a change which does not contradict the whole store of 
our previously collected experiences. It never thus attains uncon- 
ditional truth, but such a high degree of probability that it is 
practically equal to certainty." ^ 

"In speaking against the empty manufacture of hypotheses, do 
not by any means suppose that I wish to diminish the real value 

1 Helmholtz, Populat' Scientific Lectures^ p. 226. 



Hypothesis. 125 

of original thoughts. The first discovery of a new law, is the 
discovery of a similarity which has hitherto been concealed in the 
course of natural processes. It is a manifestation of that which 
our forefathers in a serious sense described as 'wit'; it is of the 
same quality as the highest performances of artistic perception in 
the discovery of new types of expression. It is something which 
cannot be forced, and which cannot be acquired by any known 
method." 1 

Dr. Whewell has discussed at length the cause of the 
failure of the Greek physical philosophy. From this 
discussion we will make a few extracts : — 

" The cause of the failure of so many attempts of the Greeks 
to construct physical science is so important, that we must endeavor 
to bring it into view here ; though the full development of such 
subjects belongs rather to the Philosophy of Induction. 

" The cause of failure was not the Jteglect of facts. It is often 
said that the Greeks disregarded experience, and spun their philoso- 
phy out of their own thoughts alone ; and this is supposed by 
many to be their essential error. It is, no doubt, true that the 
disregard of experience is a phrase which may be so interpreted 
as to express almost any defect of philosophical method ; since 
coincidence with experience is requisite to the truth of all theory. 
But if we fix a more precise sense on our terms, I conceive it may 
be shown that the Greek philosophy did, in its opinions, recognize 
the necessity and paramount value of observations ; did, in its 
origin, proceed upon observed facts, and did employ itself to no 
small extent in classifying and arranging phenomena. 

" ' The way must be the same,' says Aristotle, in speaking of 
the rules of reasoning, ' with respect to philosophy, as it is with 
respect to any art or science whatever ; we must collect the facts 
and the things to which the facts happen, in each subject, and 
provide as large a supply of these as possible.' 

" We come back, again, therefore, to the question, What was 
the radical and fatal defect in the physical speculations of the 
Greek philosophical schools ? 

1 Helmholtz, Popular Scientific Lectures, p. 227. 



126 Inductive Logic. 

" To this I answer : The defect was, that though they had in 
their possession Facts and Ideas, the Ideas were not distinct 
and appropriate to the facts. 

" The peculiar characteristics of scientific ideas, which I have 
endeavored to express by speaking of them as distinct and 
appropriate to the facts, must be more fully and formally set forth 
when we come to the philosophy of the subject. In the meantime, 
the reader will probably have no difficulty in conceiving that for 
each class of Facts there is some special set of Ideas, by means of 
which the facts can be included in general scientific truths ; and 
that these Ideas which may thus be termed appropriate., must be 
possessed with entire distinctness and clearness, in order that they 
may be successfully applied. It was the want of Ideas having this 
reference to material phenomena which rendered the ancient phi- 
losophers, with very few exceptions, helpless and unsuccessful 
speculators on physical subjects." ^ 

The point which Dr. Whewell makes here seems to 
us exactly provided for in the third rule given above 
for legitimate hypotheses. The Greeks failed, because 
their conjectures were not in the lines of known uni- 
formities of nature. They sought the causes of 
phenomena in abstract and general conceptions. 

Important as is the function of hypotheses, it may 
yet be exaggerated. Thus, Professor Davis, says: — 

" It is equally obvious that all experimental observation is like- 
wise dependent on supposition. A mere trial of possible combina- 
tions to see what will come of them, without the further sugges- 
tions of a suggested supposition, can elicit nothing, save by 
chance." ^ 

But it is plain that a chemist may take the contents of 
the stomach of a murdered man, and may test succes- 
sively for arsenic, strychnine, and other poisons, with- 

1 Whewell's History of the Inductive Sciences, vol. i, pp. Z^^, 87. 

2 Inductive Logic, p. 1 59. 



Hypothesis. 127 

out any hypothesis whatever ; and that he will reach 
the truth just as quickly without an hypothesis as with 
one. In every chemical laboratory, students are taught 
a regular system of tests, by which any questionable 
substance may be quickly identified without an hypoth- 
esis. Indeed, the tendency of science is to dispense 
with hypotheses as guides in research, to cease asking 
nature "leading questions," and to carry investigations 
forward on plans that permit the facts to speak for 
themselves. It is a waste of time to frame an hypoth- 
esis before all of the facts which can be ascertained 
are in hand. 

Dr. Fowler says: — 

" Even though a hypothesis may ultimately be discovered to be 
false, it may be of great service in pointing the way to a truer 
theory. Thus, as already remarked, the circular theory of plane- 
tary motion, and the supplementary theory of epicycles and eccen- 
trics, undoubtedly contributed to the formation of the hypothesis 
which was eventually proved true. Kepler himself tried no less 
than nineteen different hypotheses before he hit upon the right 
one, and his ultimate success was, doubtless, in no slight degree 
due to his unsuccessful efforts. There is hardly any branch of 
science in which it might not be affirmed that without a number of 
false guesses true theories could never have been attained." ^ 

The service which a false hypothesis renders is rather 
moral then intellectual. The belief that one has found 
a clue to the truth tends to keep up courage, and 
courage is necessary to persistent work upon the facts. 
But the false hypothesis, in itself considered, is purely 
a disadvantage and waste of time ; it is, like every false 
scent, a diversion from the right path. In searching 

^ Inductive Logic, p. 99. 



128 Inductive Logic. 

for something, we are not likely to strike upon it at the 
first effort ; and therefore our false guesses may be 
said to be necessary to our success. Where there are 
a number of equal possibilities, one must begin some- 
where, and go on proving negatives, until the right one 
is reached. If a paper is in the desk, and there are 
four drawers, one as likely to contain it as another, the 
successive hypotheses that it is in the first, second, and 
third, will keep us looking, and when they are exploded 
we shall know that it is in the fourth. There is no abso- 
lute way to escape the tedium of testing wrong hypoth- 
eses, but we are fortunate in proportion to the fewness 
of those that we make, and the best rule is to delay in 
making any conjecture as long as possible. Grant's 
disastrous charge at Cold Harbor was necessary to his 
final victory over Lee, simply in showing that if he was 
ever to conquer, it must be in some other way ; this is 
all of the intellectual value that can ever attach to a 
false hypothesis. 



CHAPTER XIV. 
INDUCTIVE ARGUMENTS. 

Having considered the elementary steps of inductive 
investigation, we now advance to the construction of 
inductive arguments. 

A very common form of argument is that from 
Analogy. Such an argument is based upon a primary 
induction of a uniformity of resemblances. Having 
observed a certain object to have, in many respects, 
the property x, we come to think that we are upon the 
line of one of its uniformities, and that it will be found 
to have, in all respects, the property x. But ;r may 
stand for resemblance to some other object. 

As Bishop Butler has said: — 

"Probable evidence is essentially distinguished from demonstra- 
tive by this, that it admits of degrees, and of all variety of them, 
from the highest moral certainty to the very lov/est presumption. 
We cannot, indeed, say a thing is probably true upon one very 
slight presumption for it ; because, as there may be probabihties 
on both sides of the question, there may be some against it ; and 
though there be not, yet a slight presumption does not beget that 
degree of conviction which is implied in saying that a thing is 
probably true. But that the slightest possible presumption is of 
the nature of a probability, appears from hence, that such low- 
presumption, often repeated, will amount even to moral certainty. 
Thus, a man's having observed the ebb and flow of the tide to-day, 
affords some sort of presumption, though the lowest imaginable, 
that it may happen again to-morrow ; but the observation of this 
event for so many days and months, and ages together, as it has 
been observed by mankind, gives us a full assurance that it will." ^ 

1 Introduction to the Analogy of Religion. 



130 Inductive Logic. 

Now a uniformity of resemblances is just like any 
other line of uniformity, and the argument from it is 
the same. If I have often found a substance white, I 
begin to expect to find it of that color next time ; and if 
I have found it to resemble another substance in many 
respects, I expect to find more resemblances. An 
argument from Analogy, therefore, does not differ in 
any way from an argument based upon any other 
primary induction. A primary induction may be made 
that the peach trees of a certain region yield a crop 
three seasons out of four ; and this becomes the basis 
of expectation. Just so the induction may be made 
that two objects resemble each other in three respects 
out of four (or according to any other ratio), and this 
will measure the probability of resemblance in any 
unexamined instance. 

The following example of the use of the argument 
from analogy is taken from the Scientific Papers of 
Asa Gray : — 

" The most interesting ideas connected with trees are those 
suggested by their stability and duration. They far outlast all 
other living things, and form the familiar and appropriate symbols 
of long-protracted existence. ^ As tlie days of a tree shall be the 
days of my people ' is one of the most beautiful and striking figures 
under which a blessing can be conveyed. We are naturally led 
to inquire, whether there is any absolute limit to their existence. 
If not destroyed by accident, — that is, by extrinsic causes, of 
whatever sort, — do trees eventually perish, like ourselves, from 
old age? It is commonly thought, no doubt, that trees are fully 
exposed to the inevitable fate of all other living things. The 
opposite opinion seems to involve a paradox, and to be contra- 
dicted by every one's observation. But popular opinion is an 
unsafe guide ; — the more so in this case, as our ordinary concep- 
tions on the subject spring from a false analogy, which we have 



Inductive Arguments. 131 

unconsciously established, between plants and animals. This 
common analogy might, perhaps, hold good, if the tree were actu- 
ally formed like the animal, all the parts of which are created at 
once in their rudimentary state, and soon attain their fullest devel- 
opment, so that the functions are carried on throughout life in the 
same set of organs. If this were the case with the tree, it would 
hkewise die, sooner or later, of old age, — would perish from 
causes strictly analogous to those which fix a natural limit to the 
life of animals. The unavoidable induration and incrustation of 
its cells and vessels, apart from other causes, would put an early 
and sure Hmit to the life of the tree, just as it does in fact terminate 
the existence of the leaf, the proper emblem of mortality, — which, 
although it generally lives only a single season, may yet truly be 
said to die of old age. But, as the leaves are necessarily renewed 
every year, so also are the other essential organs of the plant. 
The tree is gradually developed by the successive addition of new 
parts. It annually renews not only its buds and leaves, but its 
wood and its roots ; everything, indeed, that is concerned in its 
life and growth. Thus, like the fabled ^son, being restored from 
the decrepitude of age to the bloom of early youth, — the most 
recent branchlets being placed, by means of the latest layer of 
wood, in favorable communication with the newly-formed roots, 
and these extending at a corresponding rate into fresh soil, — 

' Quae quantum vertice ad auras 
^therias, tantum radice in Tartara tendit,' 

why has not the tree all the conditions of existence in the thou- 
sandth that it possessed in the hundredth, or the tenth, year of its 
age ? The old and central part of the trunk may, indeed, decay ; 
but this is of little moment, so long as new layers are regularly 
formed at the circumference. The tree survives, and it is difficult 
to show that it is liable to death from old age in any proper sense 
of the term. Nor do we arrive at a different conclusion when we 
contemplate the tree under a less familiar but more philosophical 
aspect, — considering it not as a simple individual, like man or the 
higher animals, but as an aggregate of many individuals, which, 
though ordinarily connected with the parent stalk, are capable of 



132 Inductive Logic. 

growing by themselves, and, indeed, often do separate spontane- 
ously, and in a variety of ways acquire independent existence. If, 
then, the tree be, as it undeniably is, a complex being, an aggre- 
gate of as many individuals, united in a common trunk, as there 
are, or have been, buds developed on its surface ; and if the com- 
ponent individuals be annually renewed, why should not the 
aggregate, the tree^ last indefinitely? To establish a proper anal- 
ogy, we must not compare the tree with man, but with the coral 
formations, in which numberless individuals, engrafted and blended 
on a common base, though capable of living when detached from 
the mass, conspire to build up those arborescent structures so 
puzzling to the older naturalists that they were not inappropriately 
named ^ zoophytes,' or animal-plants. The immense coral-groves, 
which have thus grown up in tropical seas, have, no doubt, endured 
for ages ; the inner and older parts consisting of the untenanted 
cells of individuals that have long since perished, while fresh 
structures are continually produced on the surface. The individ- 
uals, indeed, perish, but the aggregate may endure as long as time 
itself. So with the tree, considered under this point of view. 
Though the wood in the center of the trunk and large branches — 
the produce of buds and leaves that have long ago disappeared 
— may die and decay, yet while new individuals are formed upon 
the surface with each successive crop of fresh buds, and placed in 
as favorable communication with the soil and the air as their pre- 
decessors, the aggregate tree would appear to have no necessary, 
no inherent limit to its existence." ^ 

The question here is, whether the analogy, the uni- 
formity of resemblance, is between the tree and an 
individual animal, or between the tree and a community 
of animals. Most readers will suspect that neither 
analogy is complete enough to justify the conclusions 
suggested. 

The relation of primary and secondary inductions in 
constructing an argument is admirably illustrated in 

1 Vol. ii, p. 79. 



Inductive Arguments. 133 

the famous incident of Robinson Crusoe's discovery of 
the solitary footprint in the sand. The story runs as 
follows: — 

" It happened one day, about noon, going towards my boat, I 
was exceedingly surprised with the print of a man's naked foot on 
the shore, whicli was very plain to be seen on the sand. I stood 
like one thunderstruck, or as if I had seen an apparition. I listened, 
I looked around me, but I could hear nothing nor see anything ; I 
went up to a rising ground to look farther ; I went up the shore 
and down the shore, but it was all one ; I could see no other 
impression but that one." 

Crusoe was already in possession of the primary 
induction, " Impressions of a given form are made only 
by men." Observation supplied the minor premise, 
" Here is an impression of the given form." The 
secondarily inductive conclusion followed, " A man 
made this." 

A more complex illustration may be taken from the 
writings of the eminent glacialist, Professor G. Frederick 
Wright : — 

"In the summer of 1882, after having the previous year 
completed, with Professor Lewis, the exploration of the glacial 
boundary through Pennsylvania, I continued to work through the 
state of Ohio, and traced the line at length to the Ohio River, 
near Ripley, about sixty miles above Cincinnati. From this point, 
for about thirty miles down the river, to the vicinity of New Rich- 
mond, the glacial boundary lies upon the north bank of its trough; 
till, bowlders, and scratched stones being found on the highlands 
down to the extreme margin on the north side, but being absent 
from the corresponding highlands on the Kentucky side. Near 
Point Pleasant, the birth-place of President Grant, the river 
makes a long bend to the north, continuing in this direction to 
Cincinnati, and thence westward to North Bend, the home and 
burial-place of President William Henry Harrison ; here it turns 



134 Inductive Logic. 

south again, thus forming in Kentucky a peninsula, as it were, 
pointing to the north, and including the territory of Campbell, 
Kenton, and Boone counties. Upon examining this district it 
was found that in places in Campbell county, and over the whole 
northern and western parts of Boone county, there were true 
glacial deposits on the highest lands — the elevation near Burling- 
ton being five hundred and fifty feet above low-water mark at 
Cincinnati. In places, large numbers of bowlders of northern 
origin were found stranded on the very summit-level of the region 
— 2.<?., on the divide, between the short streams running north and 
those running south, and between the Licking and the Ohio River. 
They were also found south of this secondary divide, seven miles 
back from the river, and five hundred feet above it (near Florence, 
Boone county). Several were recognized as belonging to a species 
of red jasper conglomerate, whose outcropping is well marked on 
the northern shore of Lake Huron and above the outlet of Lake 
Superior. These bowlders are very beautiful ; and, farther north, 
where they are more abundant in the fields, are frequently used to 
adorn the front-yards of residences or even for the construction of 
public buildings. Some of the citizens of Cleveland, Ohio, have 
brought large fragments for this purpose from the parent ledges. 
But here, beside a roadway through the Kentucky hills, were large 
specimens of this same conglomerate (one bowlder being nearly 
three feet in diameter), which had been transported by glacial ice 
fully six hundred miles from their native bed, and left to tell the 
story not only of their own travels, but of other most interesting 
events connected with the cause which transported them. These 
glacial deposits south of the Ohio are such as to make it certain 
that the front of the continental glacier itself pushed, at some 
points, seven or eight miles beyond the Ohio River ; and it is 
altogether probable that for a distance of fifty miles (or completely 
around the eastern, northern, and western sides of the Kentucky 
peninsula formed by the great bend of the river), the ice came 
down to the trough of the Ohio, and crossed it so as completely 
to choke the channel, and form a glacial dam high enough to 
raise the level of the water five hundred and fifty feet — this being 
the height of the water-shed to the south. The consequences 
following are interesting to trace. 



Inductive Arguments, 135 

" The bottom of the Ohio River at Cincinnati is 447 feet above 
the sea-level. A dam of 553 feet would raise the water in its rear 
to a height of 1000 feet above the tide. This would produce a 
long, narrow lake, of the width of the eroded trough of the Ohio, 
submerge the site of Pittsburg to a depth of 300 feet, and make 
slack water up the Monongahela nearly to Grafton, W. Va., and 
up the Alleghany as far as Oil City. All the tributaries of the 
Ohio would Ukewise be filled to this level with the back water. 
The length of this slack-water lake in the main valley, to its 
termination up either the Alleghany or the Monongahela, was not 
far from one thousand miles. The conditions were also peculiar 
in this, that all the northern tributaries head within the southern 
margin of the ice-front, which lay at varying distances to the north. 
Down these northern tributaries there must have poured during 
the summer months immense torrents of water to strand bowlder- 
laden icebergs on the summits of such high hills as were lower 
than the level of the dam." ^ 

Let US trace the inductive steps by which the 
conclusion is reached that there was once a lake in 
the valley of the Ohio. First there is the primary 
induction that, "This red jasper conglomerate is 
original only in Canada." This is proved only by an 
exhaustive examination in detail of all the rocks i7t situ 
in the whole region concerned, such examination being 
continued until the mind of the investigator is satisfied 
— a point not precisely definable. Next comes the 
primary induction, "Angular and scratched bowlders 
like these are the work of glaciers." This is a primary 
induction made by the test of agreement by observation 
upon living glaciers. The united observation of geolo- 
gists over the whole world warrants another primary 
induction, the universal negative, " No agents but 
glaciers are making scratched bowlders." Observation 

1 Ice Age in No7'th America., p. 326. 



136 Inductive Logic. 

gives us the fact, "There are angular and scratched 
pieces of this jasper conglomerate in Boone county, 
Kentucky." Next is the secondary induction, " The 
ice-sheet extended into Boone county." But the 
mathematical proposition may be affirmed, " An ice- 
sheet extending from Canada into Boone county would 
dam the Ohio River." Thus we reach at last the mixed 
induction, " The Ohio River was once closed by an 
ice-dam." Again it may be affirmed, " If there was a 
dam, there was a lake"; which leads to the mixed 
induction, " There was a lake." The validity of these 
conclusions depends wholly upon the accuracy of the 
observations, and the exhaustiveness of the exarriina- 
tions by which the universal negatives are established. 
The subject of Verification has been so luminously 
presented by Dr. Fowler that nothing more will be 
necessary than to quote his remarks : — 

" In Deductive Reasoning, especially when it involves elaborate 
calculations, there is always great danger lest we should have 
omitted to take into account some particular agency or element, 
or have miscalculated its effects, or have formed a false estimate 
of the combined effect of the various agencies or elements in 
operation. The only remedy against these possible errors, besides 
the employment of great caution in the conduct of the deductive 
process itself, is to be found in Verification, a word which, in its 
stricter sense, appears to be applied to the process of testing, by 
means of an appeal to facts, the validity of the conclusions already 
arrived at by a course of deductive reasoning. Thus it had been 
deductively inferred from the Copernican theory that the planets 
Venus and Mercury ought to pass through phases, like the moon, 
and the application of the telescope, by means of which they were 
actually seen to assume these phases, furnished a triumphant 
verification of the inference. Every occurrence of an eclipse of 
the sun or moon or of the transit or occultation of a star, when it 



Inductive Arguments. 137 

accords with the previous calculations of astronomers, is also an 
instance of Verification in this the stricter sense of the term. The 
discovery of the planet Neptune affords an excellent instance of 
the same kind. But the word is often used in a looser sense and 
extended to all cases in which an appeal is made to facts, as, for 
instance, when we perform an experiment in order to test the truth 
of a hypothesis, or where we employ the Method of Difference in 
order to supplement the characteristic uncertainty attaching to the 
employment of the Method of Agreement. Of the process denoted 
by this looser sense of the word, instances will readily occur to 
every one. Thus, the diminution in the periods of Encke's comet 
has been regarded by some astronomers (though, perhaps, errone- 
ously) as a verification of the theory that space is filled with an 
interstellar medium ; or, to take an instance from a very different 
class of subjects, the recent breaking up of the slave system in the 
Southern States of America may be regarded as a verification of 
the prediction that slave and free institutions could not long 
coexist under the same political form of government. For an 
instance of a case in which the Method of Difference is called in 
to verify a previous employment of the Method of Agreement, I 
may refer back to the inquiry into the cause of crystallization, 
already adduced in my discussion of those two methods. 

" There is a still wider appHcation of the word Verification, by 
which it is extended to any corroboration of one mode of proof by 
means of another. It thus includes a deductive proof adduced in 
corroboration of an inductive one. The most common instance of 
this kind of verification is the inclusion of a partial under a more 
general law, the partial law having been arrived at inductively, 
and it being subsequently shown that the more general law leads 
deductively to it. Thus, the phenomena of the Tides had, prior 
to the epoch of Newton, been partially explained by the inductive 
method. Newton, by deducing these phenomena from the Law 
of Universal Gravitation, not only afforded a much more complete 
explanation, but also furnished the most convincing verification of 
the results already arrived at. Similarly the laws of falling bodies 
on the earth's surface, which had already been proved inductively, 
were, from the time of Newton, brought under the law of universal 
gravitation, and proved deductively from it. The same was also 



138 Indtictive Logic. 

the case with Kepler's Laws, when they were proved deductively 
from the theorem of the central force. This mode of verification 
is recommended by Mr. Mill, under the name of the Inverse 
Deductive or Historical Method, as specially appHcable to 
generalizations on society which have been inferred inductively 
from the study of history or the observation of mankind. These 
generalizations are subsequently verified by being connected 
deductively with the general laws of mind or conduct which are 
furnished by the study of Psychology or Ethology. It is thus 
shown that the generalizations of history are such as we might 
have anticipated a priori from a general knowledge of human 
nature, and each branch of the inquiry is made in this manner to 
afford a striking confirmation of the results arrived at by the other. 
"It need hardly be remarked that any verification of one 
inductive proof by another, or of a deduction by an induction, 
should conform with the laws of deductive or inductive reasoning 
as the case may be. Verification is not a distinct mode of proof, 
but is simply the confirmation of one proof by another, sometimes 
of a deduction by an induction, sometimes of an induction by a 
deduction, and, finally, sometimes of one induction or deduction 
by another. It must also be borne in mind that the term is not 
infrequently employed to designate simply the confirmation of a 
hypothesis by an appeal to facts." ^ 

In trials at law the State sets itself to ascertain the 
truth regarding certain alleged facts. The inquiry is a 
strictly inductive one, and every part of the procedure 
must, if just, illustrate the sound principles of this 
branch of logic. Since the community cannot act 
directly, special officers are appointed to represent it. 
Everything is done by exact rules, which, although 
they seem to the thoughtless to be arbitrary, have 
been established because experience has shown that, by 
the observance of them, truth will be, in the largest 
number of cases, arrived at. 

1 Inductive Logic, pp. 249-253. 



hiductive Arguments. 139 

Any criminal charge against a man is in the first place 
submitted to a Grand Jury. This body passes upon the 
question whether the hypothesis that the accused com- 
mitted the offense charged is legitimate. It considers 
whether there are any facts otherwise unexplained, 
whether the proposed explanation will include all the 
facts known, and whether the supposition of the crime 
is the simplest explanation of the facts known of the 
accused. If the answer to each of these inquiries is 
affirmative, the Grand Jury reports " a true bill," or 
legitimate hypothesis. 

The case being brought to trial, since all inductive 
proof proceeds from observation, witnesses are brought 
to testify to their own observations. 

"Oral evidence must in all cases be direct ; that is to say — 

" If it refers to a fact alleged to have been seen, it must be the 
evidence of a witness who says he saw it ; 

" If it refers to a fact alleged to have been heard, it must be the 
evidence of a witness who says he heard it ; 

" If it refers to a fact alleged to have been perceived by any 
other sense or in any other manner, it must be the evidence of a 
witness who says he perceived it by that sense or in that manner; 

" If it refers to an opinion or the grounds on which that opinion 
is held, it must be the evidence of the person who holds that 
opinion on those grounds." ^ 

The grounds upon which testimony is accepted have 
been well set forth by David Hume in his famous essay 
"Of Miracles":— 

"All effects follow not with like certainty from their supposed 
causes. Some events are found, in all countries and all ages, to 
have been constantly joined together : others are found to have 
been more variable, and sometimes to disappoint our expectations ; 

1 Stephen's Digest of the Law of Evidence (Amer. ed.), p. 126. 



140 Inductive Logic. 

so that in our reasonings concerning matters of fact, there are all 
imaginable degrees of assurance, from the highest certainty to the 
lowest species of moral evidence. 

" A wise man, therefore, proportions his belief to the evidence. 
In such conclusions as are founded on an infallible experience, he 
expects the event with the last degree of assurance, and regards 
his past experience as ixiSS. proof oi the future existence of that 
event. In other cases he proceeds with more caution : he weighs 
the opposite experiments : he considers which side is supported 
by the greater number of experiments : to that side he inclines 
with doubt and hesitation ; and when at last he fixes his judgment, 
the evidence exceeds not what we properly call probability. All 
probability then supposes an opposition of experiments and obser- 
vations, where the one side is found to overbalance the other, and 
to produce a degree of evidence proportioned to the superiority. 
A hundred instances or experiments on one side, and fifty on 
another, afford a doubtful expectation of any event ; though a 
hundred uniform experiments, with only one that is contradictory, 
reasonably beget a pretty strong degree of assurance. In all 
cases we must balance the opposite experiments, where they are 
opposite, and deduct the smaller number from the greater, in 
order to know the exact force of the superior evidence. 

'^ To apply these principles to a particular instance ; we may 
observe, that there is no species of reasoning more common, more 
useful, and even necessary to human life, than that which is 
derived from the testimony of men, and the reports of eye-witnesses 
and spectators. This species of reasoning, perhaps, one may 
deny to be founded on the relation of cause and effect. I shall 
not dispute about a word. It will be sufficient to observe, that 
our assurance in any argument of this kind is derived from no 
other principle than our observation of the veracity of human 
testimony, and of the usual conformity of facts to the report of 
witnesses. It being a general maxim that no objects have any 
discoverable connection together, and that all the inferences which 
we can draw from one to another, are founded merely on our 
experience of their constant and regular conjunction, it is evident 
that we ought not to make an exception to this maxim in favor of 
human testimony, whose connection with any event seems, in 



Inductive Arguments. 141 

itself, as little necessary as any other. Were not the memory 
tenacious to a certain degree ; had not men commonly an inclina- 
tion to truth and a principle of probity ; were they not sensible to 
shame when detected in a falsehood : were not these, I say, 
discovered by experience to be qualities inherent in human nature, 
we should never repose the least confidence in human testimony. 
A man delirious, or noted for falsehood and villany, has no 
manner of authority with us. 

" And as the evidence derived from witnesses and human 
testimony is founded on past experience, so it varies with the 
experience, and is regarded as 3. proof or 2i probability^ according 
as the conjunction between any particular kind of report, and any 
kind of object, has been found to be constant or variable. 

" The reason why we place any credit in witnesses and histo- 
rians, is not derived from any connection which we perceive a priori 
between testimony and reality, but because we are accustomed to 
find a conformity between them. But when the fact attested is 
such a one as has seldom fallen under our observation, here is a 
contest of two opposite experiences, of which the one destroys the 
other as far as its force goes, and the superior can only operate 
on the mind by the force which remains. 

" / should not believe stich a story were it told 7Jte by Cato, 
was a proverbial saying in Rome, even during the lifetime of that 
philosophical patriot. The incredibility of a fact, it was allowed, 
might invalidate so great an authority." 

It is clear, then, that the reason why testimony is 
received is that we have made the primary induction 
that the testimony of respectable men is usually con- 
joined with fact. It makes little difference whether 
this conjunction be regarded as a fact of coexistence 
or of causation. 

When a man is charged with a crime, witnesses may 
testify directly that they perceived him commit it. 
Here the logical process is brief : Human testimony is 
true ; These witnesses testify that they saw the act of 



142 Inductive Logic, 

crime ; Therefore the man is guilty. This is a secon- 
dary induction. 

But more often we must proceed by a longer road. 
The witnesses cannot testify directly to the fact 
charged ; they can testify only to other facts which 
are related to the fact charged. Such facts are said to 
be relevant to the fact in issue. The rules of Relevancy 
are simply the statements of the primary inductions 
which lawmakers have accepted as well established, 
regarding the connections of certain kinds of facts. 
Human testimony may be accepted as true ; but if 
testimony is offered to a fact, the previous question 
must be raised whether we have any primary induction 
that the existence of the fact it is proposed to prove is 
usually connected with the existence or non-existence 
of the fact charged. In the famous Salem witchcraft 
cases, which left so dark a blot upon the early history 
of New England, the fallacy was that the relevancy of 
the facts proved to the crime charged had not been 
established by any induction. If the rulings of courts 
appear to exclude certain kinds of evidence, commonly 
accepted by private persons, it is because the primary 
induction has been made that the connection of those 
facts is uncertain, and because many persons are 
extremely careless in adopting unsubstantiated reports. 
There is nothing peculiar in the logic of courts, nor 
should a single principle be admitted, except such as 
judicious men apply in reaching their own private 
conclusions. 

The following statements of the principles of rele- 
vancy are taken from Stephen's Digest of the Law of 
Evidence : — 



Inductive Arguments. 1 43 

" Evidence may be given, in any proceeding, of any fact in issue, 
and of any fact relevant to any fact in issue unless it is 
hereinafter declared to be deemed irrelevant, 

and of any fact hereinafter declared to be deemed relevant 
to the issue whether it is or is not relevant thereto." ^ 

" Facts whether in issue or not, are relevant to each other 
when one is, or probably may be, or may have been — 
the cause of the other ; 
the effect of the other ; 
an effect of the same cause ; 
a cause of the same effect : 
or when the one shows that the other must or cannot have 
occurred, or probably does or did exist or not ; 

or that any fact does or did exist or not which in the common 
course of events would either have caused or been caused by the 
other ; 

provided that such facts do not fall within the exclusive rules 
contained in chapters iii, iv, v, vi ; or that they do fall within the 
exceptions to those rules contained in those chapters." ^ 

Illustrations. 

" (a) A's death is caused by his taking poison. The adminis- 
tration of the poison is relevant to A's death as its cause. A's 
death is relevant to the poisoning as its effect. 

"(<^) A and B each eat from the same dish and each exhibit 
symptoms of the same poison. A's symptoms and B's symptoms 
are relevant to each other as effects of the same cause. 

" {c) The question is, whether A died of the effects of a railway 
accident. 

" Facts tending to show that his death was caused by inflam- 
mation of the membranes of the brain, which probably might be 
caused by the accident ; and facts tending to show that his death 
was caused by typhoid fever, which have nothing to do with the 
accident, are relevant to each other as possible causes of tne 
same effect — A's death. 

1 Stephen's Digest^ p. 5. 

2 Ibid., p. 246. 



144 Inductive Logic. 

" (^) A is charged with committing a crime in London on a 
given day. The fact that on that day he was at Calcutta is rele- 
vant as proving that he could not have committed the crime. 

"(^) The question is, whether A committed a crime. 

" The circumstances are such that it must have been committed 
either by A, B, or C. Every fact which shows this, and every 
fact which shows that neither B nor C committed it, or that either 
of them did or*might have committed it, is relevant. 

" (/") B, a person in possession of a large sum of money, is 
murdered and robbed. The question is, whether A murdered 
him. The fact that after the murder A was or was not possessed 
of a sum of money unaccounted for is relevant, as showing the 
existence or absence of a fact which, in the common course of 
events, would be caused by A's committing the murder. A's 
knowledge that B was in possession of the money would be 
relevant as a fact, which, in the ordinary course of events, might 
cause or be one of the causes of the murder. 

" C^) -^ is murdered in his own house at night. The absence 
of marks of violence to the house is relevant to the question, 
whether the murder was committed by a servant, because it 
shows the absence of an effect which would have been caused by 
its being committed by a stranger." ^ 

" Four classes of facts, which in common life would usually be 
regarded as falling within this definition of relevancy, are excluded 
from it by the Law of Evidence except in certain cases : 

" I . Facts similar to, but not specifically connected with each 
other. (jR.es inter alias actae.^ 

" 2. The fact that any person not called as a witness has asserted 
the existence of any fact. (Hearsay.) 

"3. The fact that any person is of opinion that a fact exists. 
(Opinion.) 

"4. The fact that a person's character is such as to render 
conduct imputed to him probable or improbable. (Character.) 

" To each of these four exclusive rules there are, however, im- 
portant exceptions, which are defined by the Law of Evidence." ^ 

1 Stephen's Digest, p. 247. 

2 /^/^.j p. xiii. 



Inductive Arguments. 145 

It is plain that the reason that " hearsay is not 
evidence " is that to accept hearsay is to violate the 
fundamental rule of inductive logic, which is, Make 
sure of your observations. All the other rules of exclu- 
sion are, in like manner, based upon scientific grounds. 
The whole progress of judicial science, in the trying of 
cases, is but an increase of precision in applying the 
principles of inductive logic. 



CHAPTER XV. 



FALLACIES. 



We cannot open the subject of Fallacies in a more 
interesting way than by introducing Bacon's classic 
discussion of the "Idols" in his Novum Orgamim: — 



XXXIX. 

"There are four classes of Idols which beset men's minds. 
To these for distinction's sake I have assigned names, — calling 
the first class Idols of the Tribe; the second, Idols of the Cave j 
the third, Idols of the Market-place ; the fourth, Idols of the 
Theatre. 

XL. 

" The formation of ideas and axioms by true induction is no 
doubt the proper remedy to be applied for the keeping off and 
clearing away of idols. To point them out, however, is of great 
use ; for the doctrine of Idols is to the Interpretation of Nature 
what the doctrine of the refutation of Sophisms is to common 
Logic. 

XLI. 

" The Idols of the Tribe have their foundation in human nature 
itself, and in the tribe or race of men. For it is a false assertion 
that the sense of man is the measure of things. On the contrary, 
all perceptions as well of the sense as of the mind are according 
to the measure of the individual and not according to the measure 
of the universe. And the human understanding is like a false 
mirror, which, receiving rays irregularly, distorts and discolours 
the nature of things by mingling its own nature with it. 



Fallacies. 1 47 



XLII. 

" The Idols of the Cave are the idols of the individual man. 
For every one (besides the errors common to human nature in 
general) has a cave or den of his own, which refracts and dis- 
colours the light of nature ; owing either to his own proper and 
peculiar nature ; or to his education and conversation with others ; 
or to the reading of books, and the authority of those whom he 
esteems and admires ; or to the differences of impressions, accord- 
ingly as they take place in a mind preoccupied and predisposed 
or in a mind indifferent and settled ; or the like. So that the 
spirit of man (according as it is meted out to different individuals) 
is in fact a thing variable and full of perturbation, and governed 
as it were by chance. Whence it was well observed by Heraclitus 
that men look for sciences in their own lesser worlds, and not in 
the greater or common world. 

XLIII. 

"There are also Idols formed by the intercourse and associa- 
tion of men with each other, which I call Idols of the Market- 
place, on account of the commerce and consort of men there. 
For it is by discourse that men associate ; and words are imposed 
according to the apprehension of the vulgar. And therefore the 
ill and unfit choice of words wonderfully obstructs the understand- 
ing. Nor do the definitions or explanations wherewith in some 
things learned men are wont to guard and defend themselves, by 
any means set the matter right. But words plainly force and 
overrule the understanding, and throw all into confusion, and lead 
men away into numberless empty controversies and idle fancies. 



XLIV. 

" Lastly, there are Idols which have immigrated into men's 
minds from the various dogmas of philosophies, and also from 
wrong laws of demonstration. These I call Idols of the Theatre ; 
because in my judgment all the received systems are but so many 
stage-plays, representing worlds of their own creation after an 



I4S Inductive Logic. 

unreal and scenic fashion. Nor is it only of the systems now in 
vogue, or only of the ancient sects and philosophies, that I speak ; 
for many more plays of the same kind may yet be composed and 
in like artificial manner set forth ; seeing that errors the most 
widely different have nevertheless causes for the most part alike. 
Neither again do I mean this only of entire systems, but also of 
many principles and axioms in science, which by tradition, 
credulity, and negligence have come to be received. 

"But of these several kinds of Idols I must speak more largely 
and exactly, that the understanding may be duly cautioned. 

XLV. 

" The human understanding is of its own nature prone to sup- 
pose the existence of more order and regularity in the world than 
it finds. And though there be many things in nature which are 
singular and unmatched, yet it devises for them parallels and con- 
jugates and relatives which do not exist. Hence the fiction that 
all celestial bodies move in perfect circles ; spirals and dragons 
being (except in name) utterly rejected. Hence, too, the element 
of Fire with its orb is brought in, to make up the square with the 
other three which the sense perceives. Hence, also, the ratio of 
density of the so-called elements is arbitrarily fixed at ten to one. 
And so on of other dreams. And these fancies affect not dogmas 
only, but simple notions also. 

XLVI. 

"The human understanding when it has once adopted an 
opinion (either as being the received opinion or as being agreeable 
to itself) draws all things else to support and agree with it. And 
though there be a greater number and weight of instances to be 
found on the other side, yet these it either neglects and despises, 
or else by some distinction sets aside and rejects ; in order that by 
this great and pernicious predetermination the authority of its 
former conclusions may remain inviolate. And, therefore, it was 
a good answer that was made by one who, when they showed him 
hanging in a temple a picture of those who had paid their vows as 



Fallacies. 149 

having escaped shipwreck, and would have him say whether he did 
not now acknowledge the power of the gods, — 'Aye,' asked he 
again, ' but where are they painted that were drowned after their 
vows ? ' And such is the way of all superstition, whether in 
astrology, dreams, omens, divine judgments, or the like ; wherein 
men, having a delight in such vanities, mark the events where they 
are fulfilled, but where they fail, though this happen much of tener, 
neglect and pass them by. But with far more subtlety does this 
mischief insinuate itself into philosophy and the sciences ; in 
which the first conclusion colors and brings into conformity with 
itself all that come after, though far sounder and better. Besides, 
independently of that delight and vanity which I have described, 
it is the pecuHar and perpetual error of the human intellect to be 
more moved and excited by affirmatives than by negatives ; whereas 
it ought properly to hold itself indifferently disposed towards both 
alike. Indeed, in the establishment of any true axiom, the nega- 
tive instance is the more forcible of the two. 

XLVII. 

"The human understanding is moved by those things most 
which strike and enter the mind simultaneously and suddenly, and 
so fill the imagination ; and then it feigns and supposes all other 
things to be somehow, though it cannot see how, similar to those 
few things by which it is surrounded. But for that going to and 
fro to remote and heterogeneous instances, by which axioms are 
tried as in the fire, the intellect is altogether slow and unfit, unless 
it be forced thereto by severe laws and overruling authority. 

XLIX. 

"The human understanding is no dry light, but receives an 
infusion from the will and affections ; whence proceed sciences 
which may be called ' sciences as one would.' For what a man 
had rather were true he more readily believes. Therefore he 
rejects difficult things from impatience of research ; sober things, 
because they narrow hope ; the deeper things of nature, from 
superstition ; the light of experience, from arrogance and pride, 
lest his mind should seem to be occupied with things mean and 



150 Inductive Logic. 

transitory ; things not commonly believed, out of deference to the 
opinion of the vulgar. Numberless, in short, are the ways, and 
sometimes imperceptible, in which the affections color and infect 
the understanding. 

L. 

" But by far the greatest hindrance and aberration of the human 
understanding proceeds from the dulness, incompetency, and 
deceptions of the senses ; in that things which strike the sense 
outweigh things which do not immediately strike it, though they 
be more important. Hence it is that speculation commonly ceases 
where sight ceases ; insomuch that of things invisible there is little 
or no observation. Hence all the working of the spirits inclosed 
in tangible bodies lies hid and unobserved of men. So, also, 
all the more subtle changes of form in the parts of coarser 
substances (which they commonly call alteration, though it is in 
truth local motion through exceedingly small spaces) is in hke 
manner unobserved. And yet unless these two things just men- 
tioned be searched out and brought to light, nothing great can be 
achieved in nature, as far as the production of works is concerned. 
So, again, the essential nature of our common air, and of all bodies 
less dense than air (which are very many), is almost unknown. 
For the sense by itself is a thing infirm and erring ; neither can 
instruments for enlarging or sharpening the senses do much ; but 
all the truer kind of interpretation of nature is effected by instances 
and experiments fit and apposite; wherein the sense decides 
touching the experiment only, and the experiment touching the 
point in nature and the thing itself." ^ 

Since Inductive Logic includes all the deductive 
processes, it is liable to all of the fallacies treated of in 
works upon that branch. The fallacies peculiar to 
inductive logic are those which concern Observation 
and the making of primary inductions. 

I. Non-observation, or Prejudice. — All induction 
being based upon observation, any opinion about facts 

1 Bacon's Works, vol. viii, p. ']() sq. 



Fallacies. 151 

which does not begin in that way must be groundless. 
The student of nature must not enter the field of inves- 
tigation provided with broad generalizations ; as, that 
the effect must resemble the cause ; that whatever is 
inconceivable is false ; that the distinctions in nature 
correspond to the received distinctions in language, etc. 
A student of the Holy Scriptures, for instance, is not 
at liberty (although assured of the divine origin of 
Christianity by personal experience of its power) to lay 
down the dictum that a revelation from the God of 
truth can be mixed with none of the scientific errors 
of the times in which it was given. Nor can a student 
of anthropology, impressed with the dignity of man, 
assert, without examination, that we are not descended 
from ape-like ancestors, with pointed ears and long 
tails. 

But, since observation is laborious, and the mind is 
impatient for conclusions, all men are tempted to excuse 
themselves from the fatigue of examination and to taste 
at once the pleasure of feeling that they know. 

The most eminent leaders of inductive science have 
not escaped this fallacy. 

" Aristotle held some peculiar notions with respect to the skull. 
He says, 'that part of the head which is covered with hair is 
called the cranium ; the fore part of this is called the sinciput ; 
this is the last formed, being the last part in the body which 
becomes hard.' He correctly alludes here to the opening in the 
frontal bone of a young infant, which gradually becomes hardened 
by ossification ; 'the hinder part is the occiput, and between the 
occiput and sinciput is the crown of the head ; the brain is placed 
beneath the sinciput, and the occiput is empty (!). The skull has 
sutures; in women there is but one, placed in a circle (!) ; men have 
generally three joined in one, and a man's skull has been seen 



152 Inductive Logic. 

without any sutures at all' The often-repeated question as to how 
far Aristotle's observations are the result of his own investigation, 
naturally suggests itself again here ; had Aristotle ever dissected 
a human body, he never would have asserted a proposition so 
manifestly false as that the back of the head is empty, or that 
women have only one suture placed in a circle." ^ 

Another example can be taken from the Novum 
Organum itself: — 

"Again, it has been observed that small wooden arrows without 
an iron point, discharged from large engines, pierce deeper into 
wooden material (say the sides of ships, or the like) than the 
same arrows tipped with iron, on account of the similarity of sub- 
stance between the two pieces of wood ; although this property 
had previously been latent in the wood." ^ 

One variety of prejudice is the unquestioning accept- 
ance of an opinion as to facts upon the Authority of 
some great man. In early life, all must receive many 
things upon the authority of parents and teachers. 
But the purpose of education is wholly to remove this 
dependence, so that the adult man shall know the 
grounds of his own beliefs. The Protestant Reforma- 
tion was much more than merely a theological or 
religious movement ; it was an intellectual revolt against 
authority. Advancing thought cannot leave any part of 
the field of facts outside the scrutiny of inductive 
science, not even the facts of religion ; for in the 
domain of science there is no pope. But many Protes- 
tants still bow to authority, and those most independent 
of the authority of tradition often accept without ques- 

1 Quoted by Fowler from the Quarterly Review for January, 1865. 
Inductive Logic, p. 262. 

2 Page 226. 



Fallacies. 



153 



tion the dicta of the supposed prophets of advanced 
thought. 

In the best schools of the present day, the teacher 
imposes no dogmas by virtue of his own authority; he 
claims no exhaustive and finished knowledge of his 
subject. Simply as an older investigator, he invites the 
pupil to inspect the results already reached, and to take 
a place beside his teacher at the boundary of knowl- 
edge, and push it further outwards. That teacher fails 
in his most important duty, who does not impress his 
students with the present incompleteness of his science, 
and the inadequacy of all the text-books in use. It 
was Agassiz's custom to give to the beginner a fish and 
require him to look at it for himself ; so great a teacher 
never made the mistake of substituting his own books 
for the book of nature. 

" But an undiscriminating submission to the authority of con- 
temporaries, of which I have hitherto exclusively spoken, has 
been but a slight source of error when compared with undis- 
criminating submission to the authority of past generations. The 
latter involves a kind of compound fallacy. The authority of an 
Aristotle or a Galen has come, by the process already described, 
to be received without question and without limit by his own or by 
the succeeding generation ; and then, by the constant repetition 
of a similar process, it is received from that generation by the 
leading minds of the next, from them by their contemporaries, and 
so on, respect for tradition being blended with respect for a great 
name, and both these resting for their support on the deference 
paid to established authority. Many of the propositions accepted 
without the slightest hesitation by previous generations on this 
kind of authority now appear to us patently absurd, nor is it with- 
out effort that we can realize the universahty of their former 
reception." ^ 

1 Fowler's Inductive Logic, p. 292. 



154 hidiLctive Logic. 

" Of this tendency we have many ^ glaring instances,' as Bacon 
would call them. The error has been, so to say, canonized in the 
proverb ^ Malle/n cum Platone errare.'^ There is a characteristic 
anecdote of Scheiner, who contests with Galileo the honor of hav- 
ing been the first to observe the spots on the sun. Scheiner was 
a monk ; and, on communicating to the superior of his order the 
account of the spots, he received in reply from that learned father 
a solemn admonition against such heretical notions : ' I have 
searched through Aristotle,' he said, ^ and can find nothing of the 
kind mentioned ; be assured, therefore, it is a deception of your 
senses, or of your glasses.' " ^ 

II. Partial Observation, or the Neglect of Negative 
Instances. — This is the most subtle and dangerous of 
all the fallacies, and the hardest to correct. Practi- 
cally, the section which treats of this fallacy is the 
most important one in any text-book of inductive 
logic. As soon as a few similar phenomena are 
perceived, the mind moves naturally toward a primary 
induction. Having observed that this A and that A 
and the other A are X, the generalization is suggested 
that all ^'s are X ; sometimes, indeed, a single case is 
enough to beget an opinion. When this opinion has 
been a little while entertained, the minds of most per- 
sons seem almost wholly to lose the power to notice the 
cases in which an A is not X ; every positive instance 
is observed, and confirms the conviction, but the nega- 
tive instances are either entirely overlooked, or else 
lightly explained away. 

The following case is taken from Brachet's Historical 
Grammar of the French Tongite : — 

1 Baden Powell's History of N'atiiral Philosophy, p. 171. Quoted in 

Fowler's Inductive Logic, p. 292. 



Fallacies. 155 

" The tendency to simplify and reduce the number of cases was 
early felt in the popular Latin ; the cases expressed shades of 
thought too delicate and subtle for the coarse mind of the Bar- 
barian. And so, being unable to handle the learned and compli- 
cated machinery of the Latin declensions, he constructed a system 
of his own, simplifying its springs, and reducing the number of the 
effects at the price of frequently reproducing the same form. 
Thus the Roman distinguished by means of case-terminations the 
place where one is, from the place to which one is going : ^ veniunt 
ad domum,' 'sunt in domo.' But the Barbarian, unable to grasp 
these finer shades, saw no use in this distinction, and said, in 
either case alike, 'sum in domum,' 'venio ad domum.' 

" Thus, from the fifth century downwards, long before the first 
written records of the French language, popular Latin reduced the 
number of cases to two : (i) The nominative to mark the subject; 
and (2) that case which occurred most frequently in conversation, 
the accusative, to mark the object or relation. From that time 
onwards the Latin declension was reduced to this : — subject, 
murus ; object, muru7n. 

" The French language is the product of the slow development 
of popular Latin ; and French grammar, which was originally 
nothing but a continuation of the Latin grammar, inherited, and in 
fact possessed from its infancy, a completely regular declension; 
subject, murs^ uturiLS j object, inur, muritin j and people said, 
' ce imtrs est haut '; ' j'ai construit un inur.'' 

" This declension in two cases forms the exact difference between 
ancient and modern French. It disappeared in the fourteenth 
century, not without leaving many traces in the language, which 
look like so many insoluble exceptions, but find their explanation 
and historic justification in our knowledge of the Old French 
declension." 1 

Here it will be observed that the single instance of 
change from the full declension of nouns in Latin to 

1 Dr. Kitchin's Trans., p. 88. Seventh Edition, pp. 98-100, mistakenly 
quoted by Dr. Fowler {^Inductive Logic, p. 201) as an illustration of con- 
comitant variations. 



156 Inductive Logic. 

the non-inflection of nouns in French has suggested to 
M. Brachet the generalization that barbarians cannot 
readily understand and handle declensions. This is, of 
course, in the face of the negative facts that these same 
barbarians spoke the inflected Teutonic languages, that 
fully inflected languages are found among barbarians in 
Africa, in Arabia, and in all parts of the earth ; indeed, 
that the history of the most cultivated languages has 
been to pass from full inflection in barbarous times to 
less inflection in days of civilization. He who would 
hear the most delicate inflections of the Arabic, used 
with precision, must go among the illiterate sons of the 
desert, not into the cities. Yet very few of the readers 
of M. Brachet' s most interesting work ever think of 
these negative instances. There is, to most persons, 
something distasteful in assuming a critical attitude 
toward an author; ingenious and pleasing generaliza- 
tions find with ordinary readers unchallenged accept- 
ance. 

This fallacy is peculiarly safe from detection when, in 
a generalization, we have mistakenly put species for 
genus. For example, it was believed by many gram- 
marians of the last generation that the Greek Aorist 
tense, which almost exactly corresponds in meaning to 
the English preterite, "denotes a single or momentary 
action." Instances in which single or momentary 
actions were expressed in the aorist were common 
enough. The fallacy was exactly like that of assuming 
that all Americans are Virginians, or more precisely, 
that the name Americans belongs most naturally and 
properly to Virginians, because Virginians are Ameri- 
cans. Such cases as "These all died," where the verb 



Fallacies, 157 

is aorist, were explained as viewing a single instance 
as representative ; cases like " He abode two whole 
years in his own hired dwelling " were overlooked. 
Eminent theologians went so far as to base the proof 
of the doctrine that "we all sinned in Adam" on the 
fact that St. Paul uses the aorist in saying " all sinned " ; 
and since that must " denote a single and momentary 
action " of the whole race, it could, of course, be 
nothing else than eating the forbidden fruit in the 
garden of Eden. 

A very common definition of a verb in the grammars 
of our public schools is, "A verb is a word which 
expresses action, being, or state." Hundreds of teach- 
ers have taught this definition to their pupils without 
noticing that the three words "action," "being," and 
"state" in the definition are all negative instances; 
they express action, being, and state, and yet are not 
verbs. Such nouns as love, hate, murder, theft, peace, 
existence, etc., appear on every page, and yet it never 
occurs to these teachers that, according to their defini- 
tion, these words should be verbs. The fallacy is in 
taking that for a mark of a species which is the mark 
of the genus in which the species is included, and which 
the species in question shares with others. 

" We would strongly recommend to any of our readers whose 
occupations lead them to attend to the ' signs of the weather,' and 
who, from hearing a particular adage often repeated, and from 
noticing themselves a few remarkable instances of its verification, 
have ' begun to put faith in it,' to commence keeping a note-book, 
and to set down without bias all the instances which occur to them 
of the recognized antecedent, and the occurrence or non-occurrence 
of the expected consequent, not omitting, also, to set down the 
cases in which it is left undecided; and, after so collecting a 



158 Inductive Logic. 

number of instances (not less than a hundred), to proceed to form 
his judgment on a fair comparison of tlie favorable, the unfavor- 
able, and the undecided cases ; remembering always that the 
absence of a majority one way would be in itself an improbability^ 
and that, therefore, to have any weight, the majority should be a 
very decided one, and that not only in itself, but in reference to 
the neutral instances. We are all involuntarily much more strongly 
impressed by the fulfilment than by the failure of a prediction, and 
it is only, when thus placing ourselves face to face with fact and 
experience, that we can fully divest ourselves of this bias." ^ 

III. Malobservation. — It is possible to make care- 
ful observations, but to misunderstand what we observe. 
The simple sensations which the brain receives are 
interpreted in accordance with primary inductions more 
or less inexact. The far greater part of all our so-called 
observations are necessarily inferences, and we are 
often most in error when acting upon what seems the 
direct evidence of our own senses. Here is an example 
from the Novum Organum : — 

" On this subject, therefore, we may take the following as an 
Instance of the Fingerpost. We see in large fires how high the 
flames ascend ; for the broader the base of the flame, the higher 
is its vertex. Thus extinction appears to commence at the sides, 
where the flame is compressed and troubled by the air. But the 
heart of the flame, which is not touched by the air but surrounded 
by other flame on all sides, remains numerically identical ; nor is 
it extinguished until gradually compressed by the surrounding air. 
Thus all flame is in the form of a pyramid, being broader at the 
base where the fuel is, but sharp at the vertex, where the air is 
antagonistic and fuel is wanting. But smoke is narrow at the 
base, and grows broader as it ascends, like an inverted pyramid ; 
the reason being that the air admits smoke and compresses flame. 

1 Sir John Herschel's Familiar Lectiires on Scientific Subjects, Lecture 
IV, quoted by Fowler, Inductive Logic, p. 257. 



Fallacies, 159 

For let no one dream that lighted flame is air, when in fact they 
are substances quite heterogeneous." ^ 

Bacon in this instance did not really see what he 
thought he saw. Other illustrations have been already 
given in the chapter on Observation (page 9). 

IV. Mistake in Ai'ea. — A primary induction may be 
correct, but we may mistake its area. It is important 
to know whether the instances examined have come at 
random from all parts of the field regarding which we 
generalize. Before deciding that all lobsters are red, 
the inquirer must be sure that all his observations have 
not been confined to boiled specimens. Often it is 
possible to be sure of an induction over a certain area, 
while it is held as only provisionally true over a broader 
field. Here comes in the principle which justifies the 
applying of inductions to what are called ^^ adjacent 
cases!' Since at any moment it is unlikely that we 
have reached the boundary of our territory, there are 
probably at least a few more cases of the same sort 
between us and that boundary. If we find ourselves 
upon a line of uniformity, it is improbable that we have 
struck it just at the end. A traveler from Liverpool 
to London, having for fifty miles observed red poppies 
growing in the grain fields, will expect to see some 
more red poppies ; but he will not have so positive an 
expectation of seeing them all the way to the capital. 

Hume says : — 

" The Indian prince, who refused to believe the first relations 
concerning the effects of frost, reasoned justly ; and it naturally 
required a very strong testimony to engage his assent to facts that 

1 Page 267. 



i6o Inductive Log-ic 



arose from a state of nature with which he was unacquainted, and 
which bore so little analogy to those events of which he had 
constant and uniform experience. Though they were not con- 
trary to his experience, they were not conformable to it." 

The Indian prince simply made a mistake as to the 
area regarding which his observations qualified him to 
affirm ; and that is precisely the mistake of Hume 
himself, in his famous argument against miracles. 

The ancients made this error in studying the laws of 
motion. Mr. Mill says : — 

" This assertion [that all bodies in motion continue to move in 
a straight line with uniform velocity until acted upon by some new 
force] is in open opposition to first appearances ; all terrestrial 
objects, when in motion, gradually abate their velocity, and at 
last stop ; which, accordingly, the ancients, with their inductio 
per enumerationem siinplicejn^ imagined to be the law." ^ 

The induction which the ancients made was correct, 
and was made in the only possible way ; they only 
mistook its area. What they established was the 
universal truth under ordinary conditions ; their error 
was in supposing that the truth held under all condi- 
tions. 

V, Mistake in Isolation. — The rules for isolating 
facts of causation seem so simple, their applica- 
tion seems so easy, and their results seem so sure, 
that we are likely to forget how much their value is 
diminished by the difficulty of ascertaining whether we 
have taken account of all relevant circumstances. Dr. 
Fowler says: — 

"A bullet is fired from a gun, or a dose of prussic acid is 
administered, and an animal instantly falls down dead. There is 

1 Logic, p. 290. 



Fallacies. i6i 

no hesitation in ascribing the death to the gun-shot wound or the 
dose of poison. Nor is this confidence the effect of any wide 
experience, for if it were the first time that we had seen a gun 
fired, or a dose of poison administered, we should liave no hesita- 
tion in ascribing the altered condition of the animal to this novel 
cause ; we should know that there was only one new circumstance 
operating upon it, and consequently, that any change in its condi- 
tion must be due to that one circumstance." ^ 

This analysis is wholly incorrect. When a man falls 
dead on the street we are at a loss for a cause. Many 
events, observable and unobservable, are occurring at 
the same time ; the man may have had heart disease. 
We proceed to make an hypothesis according to the 
established rules. The first inquiry of the mind is for 
some already accepted primary induction under which 
to class the event. If a small boy should shoot off a 
Chinese fire-cracker, and at that moment some one 
should fall, we should not connect the two events, 
because we already have the induction that fire-crackers 
do not kill. 

This impossibility of knowing always whether isola- 
tion is perfect, leads to the rule that in studying any 
phenomenon, we should vary the circumstances as much 
as possible, and use each of the applicable methods of 
proof independently. Yet even then we are liable to 
err, as the following example shows : — 

" Thales of Miletus, who lived in the sixth century B.C., and 
who was called Hhe first of natural philosophers ' by TertuUian, 
and ^ the first who inquired after natural causes ' by Lactantius, 
affirmed that water was the first principle of things, perhaps, 
according to some writers, because Homer had made Okeanos the 
source of the gods. At least we are reminded of the boundless 

1 hiductive Logic, p. 151. 



1 62 Inductive Logic. 

watery chaos of older cosmogonies. This doctrine of Thales was 
not without its supporters during the Middle Ages, and, indeed, the 
convertibility of water into earth and air was not absolutely dis- 
proved until about a century ago. One of the ablest supporters 
of the dogma was Van Helmont (b. 1577, d. 1644), who affirmed 
that all metals, and even rocks, may be resolved into water ; animal 
substances are produced from it, because fish live upon it ; and 
vegetable substances may also be produced from it. This asser- 
tion he endeavored to prove by what would appear to be a very 
conclusive experiment in those days, when neither the composition 
of the air nor of water was known. . He took a willow which 
weighed five pounds, and planted it in two hundred pounds of 
earth, which he had previously carefully dried in an oven. The 
willow was frequently watered, and at the end of five years he 
pulled it up and found that its weight amounted to one hundred 
and sixty-nine pounds and three ounces. The earth was again 
dried and was found to have lost only two ounces. Thus it 
appeared that 164 pounds of wood, bark, roots, leaves, etc., had 
been produced from water alone. Hence he inferred that all 
vegetables are produced from water alone ; not knowing, as was 
afterwards proved by Priestley, that a constituent of the atmosphere, 
called carbonic acid, had furnished the soKd part of the tree, 
although, indeed, there was much water with it." ^ 

This experiment of Van Helmont was, so far as he 
could know, a rigorous application of the famous test 
of difference ; yet it wholly failed to teach the truth, 
because the supposed isolation was unreal. 

Under this head belongs the well-known fallacy Post 
hoc, ergo propter hoc. No one would have the hardi- 
hood to argue that since the group of antecedents 
ABCDEFGHIJK have been followed by the conse- 
quents Imnopqrstuv, therefore C must be the cause of 
q ; but it is often convenient for a crank or a dema- 
gogue to fasten attention upon the fact that after C 

1 Rodwell's Birth of Chemistry, p. 14. 



Fallacies. 163 

followed q, the unspoken assumption being that isolation 
is conceded, that C was the only new antecedent, and q 
the only new consequent. Thus, it is a familiar fact in 
politics that hard times, whatever may have been their 
causes, discredit the party in power, the outs arguing 
that since the present administration came into office 
money has been scarce, and wholly omitting to refer to 
speculation, drought, or any other cause of financial 
depression. 

It is a mistake in isolation to overlook the MttUiality 
of Cause and Effect. This is illustrated in the following 
remarks of Sir G. C. Lewis: — 

" An additional source of error in determining political causa- 
tion is likewise to be found in the mutuality of cause and effect. 
It happens sometimes that when a relation of causation is estab- 
lished between two facts it is hard to decide which, in the given 
case, is the cause and which the effect, because they act and react 
upon each other, each phenomenon being in turn cause and effect. 
Thus, habits of industry may produce wealth ; while the acquisi- 
tion of wealth may promote industry ; again, habits of study may 
sharpen the understanding, and the increased acuteness of the 
understanding may afterward increase the appetite for study. So 
the excess of population may, by impoverishing the laboring classes, 
be the cause of their living in bad dwellings ; and, again, bad 
dwellings, by deteriorating the moral habits of the poor, may 
stimulate population. The general intelligence and good sense of 
the people may promote its good government, and the goodness of 
the government may in its turn increase the intelligence of the 
people, and contribute to the formation of sound opinions among 
them. Drunkenness is in general the consequence of a low degree 
of intelligence, as may be observed both among savages and in 
civilized countries. But, in return, a habit of drunkenness pre- 
vents the cultivation of the intellect, and strengthens the cause out 
of which it grows. As Plato remarks, education improves nature, 
and nature facilitates education. National character, again, is 



164 Inductive Logic. 

both effect and cause ; it reacts on the circumstances from which 
it arises. The national pecuharities of a people, its race, physical 
structures, climate, territories, etc., form originally a certain char- 
acter, which tends to create certain institutions, political and 
domestic, in harmony with that character. These institutions 
strengthen, perpetuate, and reproduce the character out of which 
they grew, and so on in succession, each new effect becoming, in 
its turn, a new cause. Thus a brave, energetic, restless nation, 
exposed to attack from neighbors, organizes military institutions : 
these institutions promote and maintain a warlike spirit ; this 
warlike spirit, again, assists the development of the military 
organization, and it is further promoted by territorial conquests 
and success in war, which may be its result — each successive 
effect thus adding to the cause out of which it sprung." ^ 

1 On Methods of Observation a7id Reasoning in Politics, vol. i, p. 375, 
quoted by Fowler, Inductive Logic, p. 322. 



CHAPTER XVI. 
THE WORK OF BACON. 

Two great names stand out conspicuous beyond all 
others in the development of Inductive Logic : they are 
those of Bacon and of Mill. Of the latter enough has 
already been said to give the reader a knowledge of the 
main points of his doctrine. The last chapter contains 
a long quotation which well represents the style of the 
Novum Organum. But it seems undesirable to close 
this book without devoting a brief chapter to an esti- 
mate of the debt which we owe to that " Prince of 
Philosophers," who, with the " Prince of Poets," accord- 
ing to Lord Macaulay, "made the Elizabethan age a 
more glorious and important era in the history of the 
human mind than the age of Pericles, of Augustus, or 
of Leo." 

Francis Bacon, Baron Verulam (i 561-1626), is com- 
monly regarded as the founder of modern inductive 
science. Reid expresses this opinion as follows : — 

" After man had labored in the search of truth near two thou- 
sand years by the help of Syllogisms, Lord Bacon proposed the 
method of Induction a^ a more effectual engine for that purpose. 
His Novinn Orgamcin gave a new turn to the thoughts and labors 
of the inquisitive, more remarkable and more useful thsn that 
which the Organon of Aristotle had given before, and may be 
considered a second grand era in the progress of humau nature." ^ 

1 Hamilton's Reid, p. 712 ; quoted by Minto, Logic, p. 244. 



1 66 Inductive Logic. 

This is Bacon's own claim ; he says : — 

"All those who before me have applied themselves to the 
invention of arts have but cast a glance or two upon facts and 
examples and experience, and straightway proceeded, as if inven- 
tion were nothing more than an exercise of thought, to invoke 
their own spirits to give them oracles. I, on the contrary, dwell- 
ing purely and constantly among the facts of nature, withdraw my 
intellect from them no further than may suffice to let the images 
and rays of natural objects meet in a point, as they do in the sense 
of vision ; whence it follows that the strength and excellency of 
the wit has but little to do in the matter. And the same humihty 
which I use in inventing I employ likewise in teaching. For I do 
not endeavor either by triumphs of confutation, or pleadings of 
antiquity, or assumption of authority, or even by the veil of 
obscurity, to invest these inventions of mine with any majesty ; 
which might easily be done by one who sought to give lustre to 
his own name rather than light to other men's minds. I have not 
sought (I say), nor do I seek either to force or ensnare men's 
judgments, but I lead them to things themselves and the concord- 
ances of things, that they may see for themselves what they have, 
what they can dispute, what they can add and contribute to the 
common stock. And for myself, if in anything I have been either 
too credulous, or too httle awake and attentive, or if I have fallen 
off by the way and left the inquiry incomplete, nevertheless I so 
present these things naked and open, that my errors can be 
marked and set aside before the mass of knowledge be further 
infected by them ; and it will be easy, also, for others to continue 
and carry on my labors. And by these means I suppose that I 
have established forever a true and lawful marriage between 
the empirical and rational faculty, the unkind and ill-starred 
divorce and separation of which has thrown into confusion all the 
affairs of the common family." ^ 

The claim of Bacon to be the very first cannot be 
allowedj but he remains the great prophet and leader of 
inductive investigation. 

1 Preface to the Nozuon Organum. 



The Work of Bacon. 167 

The truth is thus stated by Minto : — 

" Undoubtedly Bacon's powerful eloquence and high pohtical 
position contributed much to make the study of Nature fashionable. 
He was high in place and great in intellect, one of the command- 
ing personalities of his time. Taking ' all knowledge for his 
province,' though study was really but his recreation, he sketched 
out a plan of universal conquest with a clearness and confidence 
that made the mob eager to range themselves under his leadership. 
He was the magnificent demagogue of science. There had been 
champions of ' Induction' before him, but they had been compara- 
tively obscure and tongue-tied. 

"While, however, we admit to the full the great services of this 
mighty advocate in making an ^ Inductive ' method popular, we 
should not forget that he had pioneers even in hortatory leader- 
ship. His happiest watchword, the Interpretation of Nature, as 
distinguished from the Interpretation of Authoritative Books, was 
not his invention. If we read Whewell's History of the Iiidiictive 
Sciences^ we shall find that many before him had aspired to 'give 
a new turn to the labors of the inquisitive,' and in particular to 
substitute inquisition for disquisition. 

" One might compile from Whewell a long catalogue of eminent 
men before Bacon who held that the study of Nature was the 
proper work of the inquisitive : Leonardo da Vinci (1452-15 19), 
one of the wonders of mankind for versatility, a miracle of excel- 
lence in many things, painter, sculptor, engineer, architect, astrono- 
mer, and physicist; Copernicus (1473-1543), the author of the 
Heliocentric theory ; Telesius (i 508-1 588), a theoretical reformer, 
whose De Remtin Natiira (1565) anticipated not a little of the 
N'ovum Orgaiiitm J Cesalpinus (i 520-1 603), the Botanist ; Gilbert 
(i 540-1 603), the investigator of Magnetism. By all these men 
experiment and observation were advocated as the only way of 
really increasing knowledge. They all derided mere book-learning. 
The conception of the world of sense as the original MS. of which 
systems of philosophy are but copies, was a familiar image with 
them-" 1 

1 Minto's Logic, Inductive and Dedicctive, pp. 245, 246. 



1 68 Inductive Logic. 

Mr. Mill has made the following judicious criticism 
upon the work of Bacon:-— 

" It has excited the surprise of philosophers that the detailed 
system of inductive logic, which this extraordinary man labored 
to construct, has been turned to so little direct use by subsequent 
inquirers, having neither continued, except in a few of its gener- 
alities, to be recognized as a theory, nor having conducted in 
practice to any great scientific results. But this, though not 
unfrequently remarked, has scarcely received any plausible explana- 
tion ; and some, indeed, have preferred to assert that all rules of 
induction are useless, rather than suppose that Bacon's rules are 
grounded upon an insufficient analysis of the inductive process. 
Such, however, will be seen to be the fact, as soon as it is con- 
sidered, that Bacon entirely overlooked Plurahty of Causes. All 
his rules imply the assumption, so contrary to all we now know 
of nature, that a phenomenon cannot have more than one cause. 

" When Bacon is inquiring into what he terms i\\Q forma calidi 
aut frigidi^ gravis aut levis^ sicci aut humidi^ and the like, he 
never for an instant doubts that there is some one thing, some 
invariable condition, or set of conditions, which is present in all 
cases of heat, or of cold, or of whatever other phenomenon he is 
considering ; the only difficulty being to find what it is ; which, 
accordingly, he tries to do by a process of elimination, rejecting 
or excluding, by negative instances, whatever is not the fo7'7na or 
cause, in order to arrive at what is. Butj^ that tliis forma or 
cause is one thing, and that it is the same in all hot objects, he 
has no more doubt of than another person has that there is always 
some cause or other. In the present state of knowledge it could 
not be necessary, even if we had not already treated so fully of the 
question, to point out how widely this supposition is at variance 
with the truth. It is particularly unfortunate for Bacon that, 
falling into this error, he should have fixed almost exclusively 
upon a class of inquiries in which it was especially fatal, namely, 
inquiries into the causes of the sensible qualities of objects. For 
his assumption, groundless in every case, is false in a peculiar 
degree with respect to those sensible qualities. In regard to 
scarcely any of them has it been found possible to trace any unity 



The Work of Bacon. 169 

of cause, any set of conditions invariably accompanying the 
quality. The conjunctions of such quaUties with one another 
constitute the variety of Kinds, in which, as already remarked, 
it has not been found possible to trace any law. Bacon was 
seeking for what did not exist. The phenomenon of which he 
sought for the one cause has oftenest no cause at all, and when it 
has, depends (as far as hitherto ascertained) upon an unassignable 
variety of distinct causes." 1 

1 Logic, p. 532. 



INDEX. 



Adjacent cases, 159. 

Agassiz, 50, 153. 

Agreement, canon for test of, 99. 

method of, 104. 

Agreement and difference, method 
of, 104. 

Ancient and modern thinking, 113. 

Anima and dme, 43. 

Aorist tense, 156. 

Applied sciences, 2. 

Area, mistake in, 159. 

Argument from facts of resem- 
blance, 42. 

Arguments, inductive, 129. 

Aristotle on the skull, 15. 

Athletic training, 96. 

Authority, 152. 

Bacon, work of, 165. 

claim of, 166. 

on " Idols," 146. 

on observation, 9. 

Bain quoted, 21. 

views discussed, 23, 31. 

Barbarians and inflections, 156. 
Blucher at Waterloo, 109. 
Botanical names, 53. 
Botany, 48. 
Brachet quoted, 154. 
Butler quoted, 129. 

Canons for isolating, 91. 
Canon for test of difference, 93. 
for test of agreement, 99. 



Cases under Canon First, 94. 

under Canon Second, loi. 

Cato, 141. 
Causation, 55, 71. 

Mill's doctrine of, 75. 

Cause simultaneous with effect, 84. 

the sum of conditions, 85. 

Chemical nomenclature, 53. 

Chinamen, 40. 

Classes of inductions, 31. 

Classification, 52. 

Cliffs of England, 17. 

Coexistence, facts of, 7, 47. 

Color in animals, 39. 

Comprehensive cause, 91. 

Concomitant variations, 105, iii. 

Conditional cause, 61. 

Copernicus, 37. 

Correction of instances, 106. 

Cretans, 17. 

Crows, 17, 38, 115. 

Crucial instances, 39. 

Crusoe, Robinson, 133. 

Crystallization, 108. 

Dana on coral islands, 121. 
Darwin quoted, 11, 69, 117. 

on coral islands, 121. 

on species, 51. 

Davis quoted, 16, 73, 126. 

on induction, 31. 

Deductive logic, relation to in- 
ductive, 2. 
Dew, cause of, no. 



172 



Index. 



Difference, canon for test of, 93. 
Discovery, 4. 
Dragon not a fact, 6. 

Ebullition in hydrochloric acid, 

102. 
Efficient cause, 64. 
Empirical cause, 93. 

laws, 25, 34, 116. 

Energetic cause, 60. 

Eohippus, 44. 

Events, the causes of events, 65. 

the reactions of things, 91. 

Evidence at law, 139. 
Exception proves the rule, 25. 
Experience tests uniformities, 19. 
" Experimental " not appropriate 

name for Mill's methods, 107. 
Explanation, 116. 

Facts, 6. 

of causation, 7, 55. 

of coexistence, 7, 47. 

of relation, 6. 

of resemblance, 7, 41. 

of succession, 8, 55. 

ultimate, 8. 

Fallacies, 146. 

Final cause, 70. 

Firecracker, 161. 

Forma, Bacon's inquiry for, 168. 

Fowler quoted, 11, 12, 18, 43, 136, 

160. 
view of inductio per enume- 

rationem siniplicen, 18, 30. 
Formal cause, 70. 
Friction, heat by, iii. 

Genesis of the horse, 44. 
Glacial dam at Cincinnati, 133. 
Gold, 47. 
Grand jury, 139. 



Grant at Cold Harbor, 128. 
Gratuitous hypothesis, 118. 
Gray quoted, 49, 130. 
Greek physical philosophy, 125. 

Hazard of induction, 22. 

Hearsay, 145. 

Helmholtz, on hypothesis, 124. 

Herschel quoted, 37, 157. 

Historical cause, 66. 

Horse, 44. 

Hume quoted, 139, 159. 

as to miracles, 160. 

Huxley, 117. 
Hypothesis, 37, 115. 

importance of, 126. 

Mill's definition, 119, 

value of false, 127. 

Ice and salt, 74. 

" Idols," Bacon's, 146. 

Inductio per emmierationem sini- 
pliceni, 17, 19, 113, 160. 

Induction defined, 14. 

Inductions of modern science, 
24. 

Inductive arguments, 129. 

Inductive logic defined, i. 

relation to deductive, 2. 

Indian prince, 1 59. 

Indirect method of agreement, 104, 
109. 

Inference from particulars to par- 
ticulars, 33. 

from single instances, 38. 

Iodine, 100. 

Iron in oxygen, 92. 

Isolating, canons for, 91. 

Isolation, mistake in, 160. 

Joint method of agreement and 
difference, 104, 109. 



Index. 



173 



Latin quantities, 26. 
Laws of nature, 116. 
Le Conte quoted, 44, 121. 
Legitimate hypothesis, 118. 
Lewis quoted, 163. 
Linnseus, 48. 
Lotze quoted, 63. 

Marble in acid, 95. 
Master's degree, 96. 
Masts and hulls of ships, 36. 
Material cause, 61. 
Method of agreement, 104. 

of difference, 104. 

of agreement and difference, 

104. 

of residues, 104. 

concomitant variations, 105, 

III. 
Mill quoted, 12, 19, 20, 31, 34, 36, 

38, ^T, 78, 81, 85, 87, 103, 104, 

108, no, 112, 119, 168. 
Mill, cause and effect sometimes 

simultaneous, 81. 

definition of cause, 77. 

doctrine of causation, 75. 

four experimental methods, 

103. 

on hypothesis, 119. 

on inductio per emimerationetn 

simp lie em, 18. 
infers from particular to par- 
ticular, 2>Z- 

misses sequence, 108. 

on the will, 87. 

on the root of the theory of 

induction, 47. 

vagueness of his canons, 107. 

mental characteristics, 32. 

Mill and river, 16. 

Minto, 31, quoted, 33, 116, 167. 

Mistake in area, 1 59. 



Mistake in isolation, 160. 
Mixed inductions, 14, 36. 
Motion, laws of, 160. 
Murray on coral islands, 123. 
Mutuality of cause and effect, 163. 

Natural kinds, 48. 

Negative cause, 70. 

Neglect of negative instances, 1 54. 

Neptune, 120. 

Newton's discoveries, 36. 

Night the cause of day, 86. 

Nomenclature, 53. 

Non-observation, 150. 

Noun or verb the cause, 109. 

Observation, 9. 

characteristic of induction, 9. 

contrasted with experiment, 

10. 
Occasional cause, 68. 
Opium, 43. 

Partial observation, 154. 

Perceptions confused with infer- 
ences, 12. 

Planets, 22. 

Plurality of causes, 102. 

Poppies, 159. 

Pottery, 42. 

Post hoc, ergo propter hoc, 162. 

Prejudice, 150. 

Present tense, 15. 

Primary inductions, 14, 20, 29. 

Primary rule for inductive thinking, 
II. 

Probable evidence, 129. 

Problem of induction solved, 39. 

Pure inductions, 14. 

Pure sciences, 2. 

Reid on Bacon, 165. 
Relevancy, 142. 



174 



Index. 



Resemblance, facts of, 7, 41. 
Residue, same as difference, 106. 
Residues, method of, 104. 
Rodwell quoted, 162. 
Rubidium, 28, 39. 
Rumford quoted, 56. 

his experiment discussed, 59. 

Root of the theory of induction, 47. 

Secondary inductions, 28. 

Scheiner, 154. 

Schiller quoted, 100. 

Ship and iceberg, 119. 

Solidification and crystallization, 
109. 

Socrates, 29. 

Species, 49. 

Agassiz on, 51. 

Darwin on, 51. 

De Candolle on, 51. 

Gray on, 49. 

States, d"]. 

Stephen quoted, 139, 142. 

Stewart on observation, 13. 

Substantive facts, 6.' 

Succession confused with cau- 
sation, 56, 72. 

Succession, facts of, ']2, 

Swans, 38. 

Symbols under Canon First, 97. 

under Canon Second, loi. 

Siphon, 66. 

Tariff, 99. 

Taste and freedom, 100. 
Terminology, 53. 
Testimony, 139. 
Theory, 115. 



Things causes of events, 64. 

causes of things, 64. 

Touching a button, 94. 
Trees, longevity of, 130. 
Trials at law, 139. 

Ultimate laws, 25. 

properties, 55. 

Unconditionalness, 85. 

Uniformities, how discovered, 15. 

Uniformity of nature, 19, 33, 41, 
42. 

Uniformity not in course of events, 
20. 

Unknown not discovered by rea- 
soning, 3. 

Vagueness of Mill's canons, 107. 

Van Helmont's experiment, 161. 

Varying the circumstances, 161. 

Vera causa, 118. 

Veracity of God, 17. 

Verb defined, 157. 

Verification, 136. 

Vesuvius, 25. 

Village matron, 33, 34. 

Volitional cause, 62. 

Weather on Lake Erie, 26. 

signs of, 157. 

Webster, 95. 
Whately quoted, 4. 

on induction, 30, 31. 

Whewell on Greek philosophy, 125. 
Will and wish, 90. 
Willow, 162. 
Wooden arrows, 152. 
Wright quoted, 133. 



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146 PHILOSOPHY. 



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Ouilines of Metaphysic. 

This work consists of three parts — Ontology, Cosmology, Phenomenol- 
ogy. The first part contains chapters on the Conception of Being, the 
Content of the Existent, Reality, Change, and Causation ; the second 
treats of Space, Time, Motion, Matter, and the Coherency of Natural 
Events; the third, of the Subjectivity and Objectivity of Cognition. 

Outlines of the Philosophy of Religion. 

Lotze here discusses the Proof for the Existence of God, the Attributes 
and Personality of the Absolute, the Conceptions of the Creation, the Pre- 
servation and the Government of the World, and of the World-time. 

Outlines of Practical Philosophy. 

This contains a discussion of Ethical Principles, Moral Ideals, and the 
Freedom of the Will, and then an application of the theory to the Indi- 
vidual, to Marriage, to Society, and to the State. Many interesting 
remarks on Divorce, Socialism, Representative Government, etc., abound 
throughout the volume. 

Outlines of Psychology. 

The Outlines of Psychology treats of Simple Sensations, the Course of 
Representative Ideas, of Attention and Inference, of Intuitions, of Objects 
as in Space, of the Apprehension of the External World by the Senses, of 
Errors of the Senses, of Feelings, and of Bodily Motions. Its second part 
discusses the nature, position, and changeable states of the Soul, its rela- 
tions to time, and the reciprocal action of Soul and Body. 

Outlines of /Esthetics. 

The Outlines of Esthetics treats of the theory of the Beautiful and of 
Phantasy, and of the Realization and Different Species of the Beautiful. 
Then follow brief chapters on Music, Architecture, and Poetry. 

Outlines of Logic. 

This discusses both pure and applied Logic. The Logic is followed by a 
brief treatise on the Encyclopaedia of Philosophy, in which are set forth 
the definition and method of Theoretical Philosophy, of Practical Phi- 
losophy, and of the Philosophy of Religion. This volume makes an 
admirable brief text-book in Logic. 



PHILOSOPHY. 147 

Our Notions of Number and Space. 

By Herbert Nichols, recently Instructor in Psychology in Harvard 
University. Assisted by William E. Parsons. 12mo. Cloth, vi + 
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n^HIS book is an experimental contribution to the Genetic Theory 

of Mind. It seeks to trace out the origin and development of 

our present perceptions — particularly those of ^Number and of 

Space — from the nature of our past experiences. Our experiences 

vary, for different regions of our limbs and body, according to 

their anatomy and use. Our perceptions of the same outer facts 

vary according to the regions which mediate them. The present 

work by coupling these two truths, and studying the parallel 

variations in each topographically, seeks to determine the intimate 

nature of perceptions and judgments in general. 

The Philosophical Review, 

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The Review aims to combine an impartiality and catholicity 
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148 PHILOSOPHY. 

A Brief History of Greek Philosophy. 

By B. C. Burt, M.A., formerly Decent of Philosophy, Clark University. 
12mo. Cloth. xiv+ 296 pages. Mailing price, $1.25; for introduction, 

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^HIS work attempts to give a concise but comprehensive account 
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well as purely historical. The volume contains a full topical 
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numerous foot-notes. 



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the subject. 



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of Education : I have found this 
work in philosophy to possess high 
merit. His grasp of the history of 
the subject is rare and trustworthy. 

The Modalist: or, ne Laws of Rational conviction. 

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Hamilton College, N.Y. 8vo. Cloth. 337 pages. Mailing price, 
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the thouQ'ht of Lotze. 



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PHILOSOPHY. 149 

ETHICAL SERIES. 

UNDER THE EDITORIAL SUPERVISION OF 

Professor E. Hershey Sxeath of Yale University. 

T^HE primary object of the series is to facilitate the study of the 
History of Ethics in colleges. This History will be in the 
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All teachers will doubtless concede the advisability of placing 
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sitions — such as are contained in the various Histories of Ethics. 
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of systems are to be studied. The series will make provision for 
these difficulties by presenting each system in carefully edited 
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See also the Announcements. 

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rPHE present volume contains the whole of the third book of the 
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The analysis and criticism of his system follows lines somewhat 
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in another light. In all respects it is hoped that the volume may 
prove helpful to those who wish to study the ethical system of 
Kant's predecessor. 



150 



PHILOSOPHY. 



The Ethics of Hegel, 



Translated Selections from his "Rechtsphilosophie." With an Intro- 
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in the Columbian University, Washington, D.C. 12mo. Cloth, xii-i-216 
pages. Mailing price, $1.10 ; foy introduction, $1.00. 

rpHE great revival of interest and work in the department of 
Ethics during the present quarter of a century has had its 
chief inspiration and source in the idealistic philosophy of Ger- 
many. Of this philosophy Hegel was the culmination and crown. 
Apart from the empirical evolutionary school, nearly all the 
prominent writers on Ethics in England have been following 
quite the spirit and substance of Hegel. 

These " Selections " have been made from his Philosophie des 
Mechts, embracing one-half of its contents, supplemented with some 
extracts from his Plidnomenologie des Geistes, Philosophie des Geistes 
and his Philosophy of Plistory (translation). 



E. H. Capen, President of Tufts 
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bution to the department of ethical 
studies. I expect to find it useful in 
my own classes. 



G. B. Newcomb, Professor of 
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City of New York : Its value for 
students is much enhanced by the 
clear and readable introduction. 



The Psychic Factors of Civilization. 

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in social phenomena. 



Edward A. Eoss, Professor of 
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and original book that touches 
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New York Times : The book gives 
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history and the knowledge of exist- 
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sentiments culled from the great 
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